9514 1404 393
Answer:
A. yes
Step-by-step explanation:
The diagonals of a rectangle are congruent and bisect each other.
The diagonals of a parallelogram bisect each other. If they are also congruent, then the parallelogram is a rectangle.
Answer:
Yes.
Step-by-step explanation:
Press option yes
The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected? The slant height of the larger cone is equal to the slant height of the smaller cone. The slant height of the larger cone is double the slant height of the smaller cone. The slant height of the larger cone is 4 times the slant height of the smaller cone. The slant height of the larger cone is 8 times the slant height of the smaller cone.
Answer:
The slant height of the cone affected is two times the slant height of original cone
Step-by-step explanation:
we know that
If the height and base radius of a cone are increased by a factor of to create a similar cone
then
the scale factor is equal to
therefore
the slant height of the cone affected is equal to the slant height of the original cone multiplied by the scale factor
Find the slant height of the original cone
Let
l-----> slant height of original cone
la-----> slant height of the cone affected
Applying the Pythagoras theorem
so
The slant height of the cone affected is two times the slant height of original cone
(I GOT THIS FROM SOMEONE ELSES ANSWER IN 2017 SO I HOPE THIS HELPS)
The slant height of the larger cone is double the slant height of the smaller cone.
Option B is the correct answer.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3 πr²h
We have,
The slant height of the cone is affected by a factor of 2.
When the height and base radius of a cone are multiplied by 2, the dimensions of the new cone are doubled.
Therefore,
The slant height of the larger cone is double the slant height of the smaller cone.
Learn more about cones here:
https://brainly.com/question/13798146
#SPJ5
Please help ASAP !!! Thank you !
from an observer o, the angles of elevation of the bottom and the top of a flagpole are 40° and 45° respectively.find the height of the flagpole?
Answer:
Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.
We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.
Remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
So, if we define H as the height of the cliff
X as the distance between the observer and the cliff
and h as the height of the flagopole
we can write:
tan(40°) = H/X
tan(45°) = (H + h)/X
Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.
But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.
We want to find the value of h.
If we take the quotient between both equations, we get:
Tan(45°)/Tan(40°) = (H + h)/H
1.192 = (H + h)/H
1.192*H = H + h
1.192*H - H = h
0.192*H = h
So the height of the flagpole is 0.192 times the height of the cliff.
for the equation (x+3)(x+1)=1 explain why the solutions are not -3 and -1
Answer:
Step-by-step explanation:
(x+3)(x+1)=1
x²+3x+x+3=1
x²+4x+2=0
x²+4x+4=-2+4
(x+2)²=2
x+2=±√2
x=2+√2
and x=2-√2
so x≠-3
and x≠-1
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.06. If 235 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.04
Answer:
0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose the true proportion is 0.06.
This means that [tex]p = 0.06[/tex]
235 are sampled
This means that [tex]n = 235[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.06[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.06*0.94}{235}} = 0.0155[/tex]
What is the probability that the sample proportion will differ from the population proportion by greater than 0.04?
Proportion below 0.06 - 0.04 = 0.02 or above 0.06 + 0.04 = 0.1. Since the normal distribution is symmetric, these probabilities are equal, which means that we can find one of them and multiply by 2.
Probability the proportion is below 0.02.
p-value of Z when X = 0.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.06}{0.0155}[/tex]
[tex]Z = -2.58[/tex]
[tex]Z = -2.58[/tex] has a p-value of 0.0049.
2*0.0049 = 0.0098
0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04
Mrs. Taylor is planning a pizza party for her students. She plans to purchase cheese pizza and pepperoni pizza for her students to enjoy. Cheese pizzas cost $8 each and pepperoni pizzas cost $11 each. She needs to purchase at least 12 pizzas, while spending no more than $180.
What are two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit?
Let x represent the number of cheese pizzas purchased and y represent the number of pepperoni pizzas purchased.
Answer:
Step-by-step explanation:
She needs 12 pizzas
x + y = 12
She also can't spend more than 180 dollars.
8x + 11y < 180 She can get all 12 pizzas and have the bill come to 132 dollars
11 * 12 = 132
She could really be kind to her pocket book and get all cheese pizzas
8*12 = 96 which saves her 36 dollars.
So any number of either kind will do.
(0,12) = 132
(1,11) = 8*1 + 11*11 = 129
and so on down the line
A study of the pay of corporate chief executive officers (CEOs) examined the increase in cash compensation of the CEOs of 104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%. Is this good evidence that the mean real compensation μ of all CEOs increased that year? The hypotheses are
Answer:
The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.
Step-by-step explanation:
At the null hypothesis, we test if there was no increase, that is, the mean is 0, so:
[tex]H_0: \mu = 0[/tex]
At the alternative hypothesis, we test if there was an increase, that is, the mean is greater than 0, so:
[tex]H_1: \mu > 0[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%.
This means that [tex]n = 104, X = 6.9, s = 55[/tex]
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.9 - 0}{\frac{55}{\sqrt{104}}}[/tex]
[tex]t = 1.28[/tex]
P-value of the test:
The p-value of the test is a right-tailed test(test if the mean is greater than a value), with 104 - 1 = 103 df and t = 1.28.
Using a t-distribution calculator, this p-value is of 0.1017.
The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.
The salaries of 235 nurses were recorded and analyzed. The analyst later found that the highest salary was incorrectly recorded as 10 times the actual amount. After the error was corrected, the report showed that the corrected value was still higher than any other salary. Which sample statistic must have changed after the correction was made?
The sample statistic that must have changed after the correction was made is mean. Because mean is based on all the observation in the data. So changing any value in the data will impact mean.
Changing the highest salary in the data will have no impact on median because median lies at the center of data.
Changing the highest salary in the data will have no impact on mode because mode is the most frequently occurring value in the data.
Changing the highest salary in the data will have no impact on minimum because minimum is the smallest value in the data.
Hence the only statistic which will change is mean.
Answer: A-Mean
Step-by-step explanation:
A.) Mean
B.) Median
C.) Mode
D.) Minimum
The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1)is the number of hours spent studying, and the second independent variable (x2) is the student's GPA
Effects on ACT Scores
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
Step 2 of 2: Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.
Answer:
Pvalue = 0.1505
y = 0.550x1 + 3.600x2 + 7.300
Step-by-step explanation:
Given the data :
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Using technology, the Pvalue obtained using the Fratio :
F = MSregression / MSresidual = 30.228571/ 8.190476 = 3.69
The Pvalue for the regression equation is:
Using the Pvalue from Fratio calculator :
F(1, 3), 3.69 = 0.1505
Using the Pvalue approach :
At α = 0.01
Pvalue > α ; Hence, we fail to reject H0 and conclude that ; There is not enough evidence to show that the relationship is statistically significant.
The regression equation :
y = A1x1 + A2x2 +... AnXn
y = 0.550x1 + 3.600x2 + 7.300
x1 and x2 are the predictor variables ;
y = predicted variable
4
On a plan with a scale of 1:50, the floor of a rectangular cupboard is
shown with dimensions 25 cm by 3.6 cm. What are the actual dimensions
of the floor? Give your answers in metres.
Anyone know the answer ?
Answer:
The actual dimensions of the floor are 12,5m by 1,8m.
Step-by-step explanation:
Scale problems are solved by proportions, using a rule of three.
Scale of 1:50
This means that each cm on the cupboard has a real dimension of 50 cm
25 cm on the cupboard:
So the real dimension is:
25*50 = 1250 cm = 12,5m
3.6 cm
The real dimension is:
3.6*50 = 160 cm = 1,8 m
The actual dimensions of the floor are 12,5m by 1,8m.
Ms. Weaver plans to decorate the bulletin board in her classroom. She purchased 30 sheets of construction paper for $0.30 per sheet, 5 boxes of thumbtacks for $0.70 per box, and 4 framed pictures for $6.00 per picture. How much money did Ms. Weaver spend for the items?
Answer:
$36.5 money ms.weaver spent for the items
translate to a system of equations but do not solve.
A non-toxic floor wax can be made from lemon juice and food grade linseed oil. The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 30 oz of floor wax?
let x represent the number of ounces of lemon juice and y represent the number of ounces of linseed oil.
complete the system of equations.
y =
x+y =
Answer:
x + y = 30
y = 2x
Step-by-step explanation:
x = number of ounces of lemon juice
y = number of ounces of linseed oil
How much of each ingredient is needed to make 30 oz of floor wax?
x + y = 30
The amount of oil should be twice the amount of lemon juice.
y = 2x
Answer:
x + y = 30
y = 2x
Find the first derivative for y = f(x). fox ) 3x² -5x-1 at a Pocat where a = 4
Answer:
Step-by-step explanation:
f(x) = 3x² -5x - 1
f'(x) =2*3x - 5*1 +0
= 6x - 5
f'(4) = 6*4 - 5
= 24 - 5
= 19
Paul writes newspaper articles. He earns a base rate of $500 per month and an additional $100 per article he writes. Last month he earned $2000.
Write an equation to determine the number of articles (a) he sold last month.
Answer:
Total earning last month with x articles is:
x*100 + 500This is same amount as 2000
The equation is:
100x + 500 = 2000Help please somebody ASAP
Answer:
[tex]\frac{-2x+11}{(x-4)(x+1)}[/tex]
Step-by-step explanation:
I don't think we can factor this so we'll have to multiply to make the denominators the same
[tex]\frac{3(x+1)}{(x^2-3x-4)(x+1)}-\frac{2(x^2-3x-4)}{(x+1)(x^2-3x-4)}\\\\\frac{3x+3-(2x^2-6x-8)}{(x^2-3x-4)(x+1)}=\frac{-2x^2+9x+11}{(x^2-3x-4)(x+1)}\\-2x^2+9x+11=(x+1)(-2x+11)\\\\x^2-3x-4=(x+1)(x-4)\\\frac{(x+1)(-2x+11)}{(x+1)(x-4)(x+1)}=\frac{-2x+11}{(x-4)(x+1)}[/tex]
Two different types of injection-molding machines are used to form plastic parts. Two random samples, each of size 300, are selected. 15 defective parts are found in the sample from machine 1 and 8 defective parts are found in the sample from machine 2. Is it reasonable to assume that both machines have the same defective rate
Answer:
No it is not since there is 15 defectice parts in 2machines and there is 8 broken parts in the one machine
Hope This Helps!!!
In the diagram, WZ=StartRoot 26 EndRoot.
On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (negative 2, 4), point X is at (2, 4), point Y is at (1, negative 1), and point Z is at (negative 3, negative 1).
What is the perimeter of parallelogram WXYZ?
units
units
units
units
Answer:
[tex]P = 8 + 2\sqrt{26}[/tex]
Step-by-step explanation:
Given
[tex]W = (-2, 4)[/tex]
[tex]X = (2, 4)[/tex]
[tex]Y = (1, -1)[/tex]
[tex]Z = (-3,-1)[/tex]
Required
The perimeter
First, calculate the distance between each point using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]
So, we have:
[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]
[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]
[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]
[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]
So, the perimeter (P) is:
[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]
[tex]P = 8 + 2\sqrt{26}[/tex]
Answer:
its D.
Step-by-step explanation:
took test
Complete the information for that object by making estimates using appropriate units of measurement of the dimensions and by getting the actual measurements using an appropriate measuring instrument.
Answer:
hlo how are u?whats ur day is going
The level of significance is the a. same as the p-value. b. maximum allowable probability of Type I error. c. same as the confidence coefficient. d. maximum allowable probability of Type II error.
Answer:
The level of significance is the
b. maximum allowable probability of Type I error.
Step-by-step explanation:
The significance level provides the maximum probability of rejecting the null hypothesis when it is true. It is the same as a type I error (also known as false-positive). This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted. It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.
Yellowstone National Park is a popular held trip destination. This year the senior class at
High School A and the senior class at High School B both planned trips there. The senior
class at High School A rented and filed 2 vans and 3 buses with 153 students. High
School Brented and nited il vans and 10 buses with 534 students. Every van had the
same number of students in it as did the buses. Find the number of students in each van
and in each bus.
Van: 39
Bus: 18
Van: 21
Bus: 21
o
Van: 27
Bus: 19
.
Van: 18
Bus: 39
Answer:
Who was the first president of United States?
in the diagram below, BD is parallel to XY. what is the value of y?
a. 70
b. 130
c. 110
d. 20
I can't see the diagram sorry.
Step-by-step explanation:
Is there supposed to be a picture attached?
Necesito ayuda con esto
Answer:
La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].
Step-by-step explanation:
Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:
[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]
[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]
[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]
La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].
Which figure can be formed from the net?
pls answer fast for brainiest !
Answer:
It should be the top right one
(with 6ft as the height)
Step-by-step explanation:
Answer:
It must be the lower to the left choice.
Step-by-step explanation:
As you can see, the net we have is composed of only triangles.
So we should be choosing a figure with a triangular base.
Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.
The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.
Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.
If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.
Hope this helps
∠A and \angle B∠B are vertical angles. If m\angle A=(5x-9)^{\circ}∠A=(5x−9) ∘ and m\angle B=(8x-30)^{\circ}∠B=(8x−30) ∘ , then find the value of x
9514 1404 393
Answer:
x = 7
Step-by-step explanation:
Vertical angles have the same measure, so ...
m∠A = m∠B
(5x -9)° = (8x -30)°
21 = 3x . . . . . . . . . divide by °, add 30-5x
7 = x . . . . . . . . . . divide by 3
Think of 5 positive integers that have a mode of 5 and 6, a median of 6 and a mean of 7.
Answer:
5,5,6,6,13
Step-by-step explanation:
Mode means most often. The 5 numbers has 2 modes 5 and 6
This means that 4 of the numbers must be 5,5,6,6
Median means the middle number must be 6
5,5,6,6,x is the only way to to get the middle number to be 6
We need to average to 7
(5+5+6+6+x) /5 = 7
(5+5+6+6+x) /5 *5= 7*5
(5+5+6+6+x) =35
22+x = 35
x = 35-22
x = 13
The other number is 13
J. Aitchison collected expenditures data for 20 randomly selected single men and 20 randomly selected single women. He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women. What is the correct alternative hypothesis?
a. Md = 0
b. μα = 0
c. ud > 0
d. Opmen — Вwomen
e. Himen > Mwomen
f. Mmen Mwomen
Answer:
The alternative hypothesis is [tex]H_1: \mu_M - \mu_W \neq 0[/tex], considering M for men and W for women.
Step-by-step explanation:
He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women.
At the null hypothesis, we test if there is not difference, that is, the difference of the mean is 0, so:
[tex]H_0: \mu_M - \mu_W = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the difference of the means is different of 0, so:
[tex]H_1: \mu_M - \mu_W \neq 0[/tex]
[tex]5.5=2\pi \sqrt{\frac{L}{9.8}[/tex]
9514 1404 393
Answer:
7.51 m
Step-by-step explanation:
The equation matches that required for finding the length of a pendulum that has a period of 5.5 seconds. We can solve for L to find the length.
[tex]5.5=2\pi\sqrt{\dfrac{L}{9.8}}\\\\\dfrac{5.5}{2\pi}=\sqrt{\dfrac{L}{9.8}}\\\\\left(\dfrac{5.5}{2\pi}\right)^2=\dfrac{L}{9.8}\\\\L=74.1125/\pi^2\approx7.509[/tex]
The length of a pendulum with period 5.5 seconds is about 7.51 meters.
Answer:
The length, L = 7.52 m.
Step-by-step explanation:
The given expression is
[tex]5.5= 2 \pi \sqrt\frac{L}{9.8}\\\\Sqauring on both the sides\\\\5.5 \times 5.5 = 4\pi^2 \times \frac{L}{9.8}\\\\L = 7.52 m[/tex]
The value of length is 7.52 m.
The diagram below is divided into equal parts. Which fraction of the parts is white?
A diagram is divided into 4 blue parts and 3 white parts.
Three-sevenths
Four-sevenths
Three-fourths
Four-thirds
Answer: This problem is a fraction since we have several equal parts that make up one whole. The problem asks us to talk about the relationship of white pieces to the whole. Since we know the whole is made up of 7 pieces (4 blue parts and 3 white parts = 7 total parts), then 7 will be our denominator (number on the bottom of the fraction).
Now that we have our number on the bottom, we need to look back at the question to carefully decide what parts of the whole we are looking at. The question wants to know how many of the parts are white. We know that 3 of the parts are white, so that is our numerator (number of the top of the fraction).
Our final answer is 3/7 or "three-sevenths." Said another way, three of the seven pieces are white.
Step-by-step explanation:
The lengths of nails produced in a factory are normally distributed with a mean of 6.13 centimeters and a standard deviation of 0.06 centimeters. Find the two lengths that separate the top 7% and the bottom 7%. These lengths could serve as limits used to identify which nails should be rejected.
Answer:
A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 6.13 centimeters and a standard deviation of 0.06 centimeters.
This means that [tex]\mu = 6.13, \sigma = 0.06[/tex]
Value that separated the top 7%:
The 100 - 7 = 93rd percentile, which is X when Z has a p-value of 0.93, so X when Z = 1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.475 = \frac{X - 6.13}{0.06}[/tex]
[tex]X - 6.13 = 1.475*0.06[/tex]
[tex]X = 6.2185[/tex]
Value that separates the bottom 7%:
The 7th percentile, which is X when Z has a p-value of 0.07, so X when Z = -1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.475 = \frac{X - 6.13}{0.06}[/tex]
[tex]X - 6.13 = -1.475*0.06[/tex]
[tex]X = 6.0415[/tex]
A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.
To teach computer programming to employees, many firms use on the job training. A human resources administrator wishes to review the performance of trainees on the final test of the training. The mean of the test scores is 72 with a standard deviation of 5. The distribution of test scores is approximately normal. Find the z-score for a trainee, given a score of 82.
Answer:
The z-score for the trainee is of 2.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean of the test scores is 72 with a standard deviation of 5.
This means that [tex]\mu = 72, \sigma = 5[/tex]
Find the z-score for a trainee, given a score of 82.
This is Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 72}{5}[/tex]
[tex]Z = 2[/tex]
The z-score for the trainee is of 2.
