The distribution of widgets from a production line is known to be approximately normal with mean 2.7 inches and standard deviation 0.25 inches. About 95% of the distribution lies between what two values?
A. 2.45 inches and 3.2 inches
B. 2.45 inches and 2.95 inches
C. 2.2 inches and 3.2 inches
D. 1.95 inches and 3.45 inches
Answers
Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.
To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81
The formula for calculating the z-score is expressed as;
[tex]z=\frac{x-\overline x}{s}[/tex] where:
[tex]\overline x[/tex] is the mean
s is the standard deviation
z is the z-scores
Given the following
[tex]\overline x[/tex]=2.7 in
s = 0.25
if z = -2.81
[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]
Similarly:
[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]
Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.
Learn more on normal distribution here: https://brainly.com/question/23418254
Related Questions
1. Plot the following points by hand or using an online graphing calculator. What is the function that best fits the points?
(0, 3), (1, 6), (2, 12), (3, 24)
•Linear
•Exponential
•Quadratic
Answers
write
the following numbers using Roman numerals 20
Answers
Step-by-step explanation:
xx is the Roman number of 20
(one x equal 10)
XX= 20
(two x’s (10+10) equals 20)
A garden table and a bench cost $717 combined. The garden table costs $67 more than the bench. What is the cost of the bench?
Answers
Subtract the difference form the total:
717 - 67 = 650
Divide the remaining amount by 2:
650/2 = 375
The bench cost$375
how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answers
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
Make mathematical expressions then, simplify ,50 is divided by 2 times one more than the difference of F and 3.
Answers
Answer:
F = 27
Step-by-step explanation:
50/2 = (F - 3) + 1
25 = F - 2
F = 27
5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ . (5 points)
Answers
Answer:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase
Step-by-step explanation:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase.
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answers
Answer:
x = 2 is the solution to x + 1.5 = 3.5
Step-by-step explanation:
x + 1.5 = 3.5
-1.5 -1.5
--------------------
x = 2
X
у
Which equation could be used to create the data shown in the
table?
1
5
O y = 5x
4
17
O y = 5x + 1
5
21
O y = 4x + 1
7
29
O y = x + 4
9
37
Answers
Answer:
C
Step-by-step explanation:
The equation that represents the table is y=4x+1
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
HURRY PLEASE!!!!!
All of the following expressions are equal except ____. 1/4^3 4^2/4^5 4^5/4^2 4^-3
Answers
Answer:
4^5/4^2
Step-by-step explanation:
We know 1/a^b = a^-b
a^b/ a^c = a^(b-c)
1/4^3 = 4^-3
4^2/4^5 = 4^(2-5) = = 4^-3
4^5/4^2 = 4^(5-2) = 4^3
4^-3
Answer:
[tex]4^{5}/5^{2}[/tex] = not the same
Step-by-step explanation:
you have the equations
[tex]1/4^{3} = 0.015625\\\\4^{2}/4^{5} = 16/1024 = 0.015625\\\\4^{5}/4^{2} = 1024/16 = 65\\\\4^{-3} = 0.015625[/tex]
if x and y are linear pair of angel then x +y=
Answers
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
Which of the two functions below has the smallest minimum y-value?
f(x) = 4(x - 6)4 + 1
g(x) = 2x3 + 28
O A. g(x)
B. f(x).
C. The extreme minimum y-value for f(x) and g(x) is --
D. There is not enough information to determine
Answers
Answer:
Answer A
Step-by-step explanation:
[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]
look at the image below
Answers
that's what I got, you can confirm if it's correct or not... I'm not sure
have a nice dayʘ‿ʘ
What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope-intercept form
A: y= 2/5x -1/5
B: y= 2/5x +1/5
C: y= -2/5x -1/5
Answers
Answer:
y = 2/5x + 1/5
Step-by-step explanation:
y = 2/5x + b
-1 = 2/5(-3) + b
-1 = -6/5 + b
1/5 = b
Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5
Answers
Solution :
Here the probability that exactly 28 out of 304 students will not graduate on time. That is
P (x = 28)
By using the normal approximation of binomial probability,
[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]
∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]
[tex]$=P(27.5 \leq x \leq 28.5)$[/tex]
That is the area between 27.5 and 28.5
Therefore, the correct option is (e). Area between 27.5 and 28.5
Please help!! The question is the image below VVV
Answers are also images after the picture.
Answers
Step-by-step explanation:
When adding two fractions with different bases (bottom numbers), we can use this function:
[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]
So, to apply this to the given question:
[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]
= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]
From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.
Multiply top using: (a + b)(c + d) = ac + ad + bc + bd= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]
Simplify.= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]
Remove parentheses.= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]
Simplify again.= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]
Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.
Factor.= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
Answer:
A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
I NEED THE ANSWER SOON PLEASE!!?!?! hopefully someone sees this
Answers
Answer:
1 and 1/25
Step-by-step explanation:
- 18 = -3x + 6
Plz help
Answers
Answer:
8 =x
Step-by-step explanation:
- 18 = -3x + 6
Subtract 6 from each side
-18-6 = -3x+6-6
-24 = -3x
Divide each side by -3
-24/-3 = -3x/-3
8 =x
Answer:
x= 8
Step-by-step explanation:
[tex]\sf{}[/tex]
=> -3x+6 = -18
=> -3x+6-6= -8-6
=> -3x= -24
=> x= 8
Determine the indicated term in the following arithmetic sequences.
1.) a subscript 5: {2, 5, 8, ...}
2.) a subscript 20: {4, 8, 12, ...}
3.) a subscript 18: {0,20,40,60, ...}
Answers
Answer:
[tex]a_5= 14[/tex]
[tex]a_{20}= 80[/tex]
[tex]a_{18}= 340[/tex]
Step-by-step explanation:
Solving (a):
We have:
[tex]a_1=2[/tex] --- first term
[tex]d = 5 -2 = 3[/tex] common difference
The 5h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_5= 2+ (5 - 1)*3[/tex]
[tex]a_5= 14[/tex]
Solving (b):
We have:
[tex]a_1 = 4[/tex] --- first term
[tex]d = 8 -4 = 4[/tex] common difference
The 20h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{20}= 4+ (20 - 1)*4[/tex]
[tex]a_{20}= 80[/tex]
Solving (c):
We have:
[tex]a_1 = 0[/tex] --- first term
[tex]d = 20 -0 = 20[/tex] common difference
The 18th term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{18}= 0+ (18 - 1)*20[/tex]
[tex]a_{18}= 340[/tex]
please help me with geometry
Answers
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
For a standard normal distribution, find:
P(z > c) = 0.058
Find c.
Answers
Answer:
1.572
Step-by-step explanation:
For a standard normal distribution,
P(z > c) = 0.058
To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;
Using technology or table,
Zscore equivalent to P(Z > c) = 0.058 is 1.572
Hence, c = 1.572
The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from
Earth's center, what would it weigh if it were 4,015 miles from Earth's center?
Answers
Answer:
weight =48.71228786pounds
Step-by-step explanation:
[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]
If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.
We know the inverse square law formula:
W₁ / W₂ = D²₂ / D²₁
Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.
So we have,
W₁ = 50
D₁ = 3,960
D₂ = 4015
We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,
So we can plug in those values as follows:
50 / W₂ = (4,015)²/ (3,960)²
To solve for W₂, we can cross-multiply and simplify as follows:
W₂ = 50 x (3,960)² / (4,015)²
W₂ = 50 x 15,681,600 / 16,120,225
W₂ = 48.547 pounds (rounded to three decimal places)
Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.
To learn more about inverse square law visit:
https://brainly.com/question/30562749
#SPJ2
A cone and a pyramid have equal heights and volumes. If the base area of the pyramid is 154cm^2, find the radius of the cone
Answers
Answer:
√154/π
Step-by-step explanation:
thể tích nón = thể tích hình chóp
1/3πr².h=1/3S.h
πr²=154(rút gọn h và 1/3)
=> r=√154/π
The radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
We have:
A cone and a pyramid have equal heights and volumes.
154 = πr²
π = 22/7
r = 7 cm
Thus, the radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.
Learn more about the cone here:
brainly.com/question/16394302
#SPJ2
6 times the sum of 5 and K
Answers
Answer:
6(5+k)
Step-by-step explanation:
The sum of 5 and k
5+k
6 times the sum
6(5+k)
6 less than six times a number is 42 what is the number
Answers
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
6x - 6 = 42
Step 2: Solve for x
[Addition Property of Equality] Add 6 on both sides: 6x = 48[Division Property of Equality] Divide 6 on both sides: x = 8Answer: -6
Step-by-step explanation:
We can create an equation based on the info given.
6-6x=42 Now you solve for x, the unknown number.
-6 -6 Subtract 6 on both sides
-6x=36
/-6 /-6 Divide by -6 on both sides
x=-6
The number is -6.
Factorize:
625a^4 + 4b^4
Answers
(625 • (a4)) + 22b4
54a4 + 22b4
Final result :
625a4 + 4b4
HELP WILL GIVE BRAINLYIST
Answers
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
OAmalOHopeO
Find Term 20 for the sequence a= 4 6 8 10......
Answers
4,6,8,10 are in A.P
a=4d=2[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]
[tex]\\ \rm\Rrightarrow a_20=42[/tex]
The table below shows the number of pets kept by the students in a class.
-----------------------------------------------------------
No. of pets | No. of students
-----------------------------------------------------------
0 | 9
1 | k
2 | 2
3 | 1
4 | 2
-----------------------------------------------------------
If the median number of pets is 1, what is the smallest value of k ?
Answers
Answer:
The answer for this question is 5
2. The cost of 5 pen is Rs 1200, find the cost of 1 pen.
Answers
Step-by-step explanation:
cost of 5 pen is Rs 1200,
cost of 1 pen is 1200/5 = Rs 240
Answer:
Rs 240
Step-by-step explanation:
1200÷5=240
