The question is incomplete. Here is the complete question.
In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)
(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.
(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.
(d) Identify any unusual events. Explain your reasoning.
Answer: (a) P(X<18) = 0.2033
(b) P(19.9<X<26.7) = 0.4505
(c) P(X>36.4) = 0.0202
(d) Unusual event: P(X>36.4)
Step-by-step explanation: First, determine the z-score by calculating:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
Then, use z-score table to determine the values.
(a) x = 18
[tex]z = \frac{18-23.3}{6.4}[/tex]
z = -0.83
P(X<18) = P(z< -0.83)
P(X<18) = 0.2033
(b) x=19.9 and x=26.7
[tex]z = \frac{19.9-23.3}{6.4}[/tex]
z = -0.67
[tex]z = \frac{26.7-23.3}{6.4}[/tex]
z = 0.53
P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)
P(19.9<X<26.7) = 0.7019 - 0.2514
P(19.9<X<26.7) = 0.4505
(c) x=36.4
[tex]z = \frac{36.4-23.3}{6.4}[/tex]
z = 2.05
P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)
P(X>36.4) = 1 - 0.9798
P(X>36.4) = 0.0202
(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.
The probability will be:
(a) 0.2038
(b) 0.4046
(c) 0.0203
(d) Event in part (c) is unusual.
According to the question,
[tex]\mu = 23.2[/tex][tex]\sigma = 6.4[/tex]Let,
"X" shows the test scores.(a)
The z-score for X=18 will be:
→ [tex]z = \frac{X- \mu}{\sigma}[/tex]
[tex]= \frac{18-23.3}{6.4}[/tex]
[tex]= -0.828[/tex]
So,
The probability will be:
→ [tex]P(X<18) = P(z < -0.828)[/tex]
[tex]= 0.2038[/tex]
(b)
The z-score for X=19.9 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{19.9-23.3}{6.4}[/tex]
[tex]= -0.531[/tex]
The z-score for X=26.7 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{26.7-23.3}{6.4}[/tex]
[tex]= 0.531[/tex]
So,
The probability will be:
→ [tex]P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)[/tex]
[tex]= 0.4046[/tex]
(c)
The z-score for X=36.4 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{36.4-23.3}{6.4}[/tex]
[tex]= 2.047[/tex]
So,
The probability will be:
→ [tex]P(X > 36.4 )= P(z > 2.047)[/tex]
[tex]= 0.0203[/tex]
(d)
Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.
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A train is running at the speed of 90 mph. The length of the train is 300 ft. How long would it take to cross a railway platform 492 ft long?
Answer:
Time = 1.45152 seconds
Step-by-step explanation:
1 foot = 0.000189 mile
300 ft = 300*0.000189
300 ft = 0.0567 miles
492 ft = 492*0.000189
492 ft = 0.092988 miles
Distance left to be covered by the train
= 0.092988-0.0567
= 0.036288 miles
Speed= 90mph
Time taken = distance/speed
Time taken= 0.036288/90
Time = 4.032*10^-4 hour
Time = 4.032*10^-4*60*60
Time = 1.45152 seconds
Which of the following represents the largest number?
A. 1.75 * 10^6
B .1.25 * 10^6
C. 2.75 * 10^5
D. 3.82 * 10^5
Answer:
A
Step-by-step explanation:
A 1.75 * 10^6 = 1750000
B 1.25 * 10^6 = 1250000
C 2.75*10^5 = 275000
D 3.82*10^5 = 82000
option A (1.75 * 10⁶) represents the largest number among the given options.
To determine which of the given numbers represents the largest number, we can compare the exponents of 10 in each option.
A. 1.75 * 10⁶
B. 1.25 * 10⁶
C. 2.75 * 10⁵
D. 3.82 * 10⁵
Comparing the exponents:
A: 10⁶
B: 10⁶
C: 10⁵
D: 10⁵
Since both options A and B have an exponent of 10⁶, we need to compare the coefficients.
1.75 is greater than 1.25, so option A (1.75 * 10⁶) represents the largest number among the given options.
Therefore, the answer is A. 1.75 * 10⁶.
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A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? 3 a. 0.22 c. 0.44 b. 0.78 d. 0.23
Answer:
.22
Step-by-step explanation:
The number of times a 3 was rolled is 44 out of 200
The experimental probability is 44/200 = .22
The frequency of rolling a 3 was 44.
So... 44/200
After dividing we get 0.22
Therefore, the answer is A
Best of Luck!
How many petals are on the graph? Find the trigonometric form of a given function.
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 43 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 29 sales representatives reveals that the mean number of calls made last week was 44. The standard deviation of the sample is 4.1 calls. Using the 0.050 significance level, can we conclude that the mean number of calls per salesperson per week is more than 43? H0: μ ≤ 43 H1: μ > 43 Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Answer:
The critical region for α= 0.05 is Z > ± 1.645
The calculated value of Z= 1.100
Step-by-step explanation:
The null and alternate hypotheses are given
H0: μ ≤ 43
H1: μ > 43 one tail test
∝= 0.05
n= 29
Standard Deviation= s= 4.1
Mean = μ0 = 44
For one tail test the z value of α= ± 1.645
The critical region for α= 0.05 is Z > ± 1.645
The test statistic is given by
z=μ0-μ/ s/√n
Z= 44-43/4.1/√29
Z= 1/4.1/√29
Z= 1.100
Since the calculated value Z= 1.100 does not fall in the critical region , We reject H0 and may conclude that the mean number of calls per salesperson per week is not more than 43
Find the distance between (8,4) and (8,8).
Answer:
From the given points above, the distance between them is 4 units.
Step-by-step explanation:
In order to find the distance between the two points, we must know the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, we plug in our numbers from the coordinate points that we are given to their respectful places.
[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]
Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.
[tex]d=\sqrt{(0)^2+(4)^2}[/tex]
Next, solve for the exponents.
[tex]d=\sqrt{0+16}[/tex]
Add the numbers in the radical.
[tex]d=\sqrt{16}[/tex]
Solve the radical.
[tex]d=4[/tex]
So, the distance between the two given points is 4 units.
An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).
Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
You are rolling a 6-sided number cube with the numbers 1 through 6. Which of the following represents the probability of rolling an even number?
0
1/6
1/2
1
Answer:
1/2
Step-by-step explanation:
The probailty of an event A is:
● P(A) = ( outcomes that give A) / (total number of possible outcomes)
Let A be the event in wich we get an even number.
● The sample space is {2,4,6}
So there are 3 possible outcomes that give A .
The six-sided dice has 6 outcomes
● { 1,2,3,4,5,6}
■■■■■■■■■■■■■■■■■■■■■■■■■■
● P(A) = 3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
i took the test
Put the following numbers in order from least to greatest: π/2,-4,0.09,17,√3,-1/7,√225
Answer:
-4, -1/7,0.09,π/2,√3 ,√225,17
Step-by-step explanation:
π/2, is approx 1.5
-4,
0.09,
17,
√3 is approx 1.7
,-1/7, is approx -.143
√225 = 15
From most negative to greatest
-4, -1/7,0.09,π/2,√3 ,√225,17
Answer:
[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]
Step-by-step explanation:
So we have the numbers:
[tex]\pi/2, -4, 0.09, 17, \sqrt3, -1/7, \sqrt{225}[/tex]
(And without using a calculator) approximate each of the values.
π is around 3.14, so π/2 is around 1.57.
17 squared is 289, so 1.7 squared is 2.89. Thus, the square root of 13 is somewhere between 1.7 and 1.8.
-1/7 can be divided to be about -0.1429...
And the square root of 225 is 15.
Now, use the approximations to place the numbers:
[tex]\pi/2\approx1.57; -4; 0.09;17;\sqrt3 \approx1.7; -1/7\approx-0.14;\sqrt{225}=15[/tex]
The smallest is -4.
Next is -1/7 or about -0.14
Followed by the first positive, 0.09.
And then with π/2 or 1.57
And then a bit bigger with the square root of 3 or 1.7.
And then with the square root of 225 or 15.
And finally the largest number 17.
Thus, the correct order is:
[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]
use the diagram to answer the question. AB corresponds to which line segment?
Answer:
DE
Step-by-step explanation:
I hope this helps!
In a genetics experiment on peas, one sample of offspring contained green peas and yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of that was expected? 350 127 3 4 The probability of getting a green pea is approximately . (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to ? Choose the correct answer below. 3 4 A. No, it is not reasonably close. B. Yes, it is reasonably close.
Complete Question
In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?
Answer:
The probability is [tex]P(g) =0.72[/tex]
Yes the result is reasonably close
Step-by-step explanation:
From the question we are told that
The number of of green peas is [tex]g = 436[/tex]
The number of yellow peas is [tex]y = 171[/tex]
The sample size is [tex]n = 171 + 436 = 607[/tex]
The probability of getting an offspring pea that is green is mathematically represented as
[tex]P(g) = \frac{g}{n}[/tex]
[tex]P(g) = \frac{436}{607}[/tex]
[tex]P(g) =0.72[/tex]
Comparing [tex]P(g) =0.72[/tex] to [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close
Gail bought 5 pounds of oranges and 2 pounds of bananas for $14. Her husband later bought 3 pounds of oranges and 6 pounds of bananas for $18. What was the cost per pound of the oranges and the bananas?
Answer:
1 pound of Oranges = $2
1 pound of Bananas = $2
Step-by-step explanation:
O = Oranges
B = Bananas
=> 5o + 2b = 14
=> 2b = 14 - 5o
=> b = 14/2 - 5/2o
=> b = 7 - 2.5o
3o + 6b = 18
=> 3o + 6( 7 - 2.5o ) = 18
=> 3o + 42 - 15o = 18
=> -12o + 42 = 18
=> -12o = -24
=> -o = -2
=> o = 2
One pound of oranges costs $2.
So,
5 (2) + 2b = 14
=> 10 + 2b = 14
=> 2b =4
=> b = 2
One pound of bananas also costs $2.
Factor the polynomial: 11x− xy +11y−x2
[tex]11x- xy +11y-x^2=\\-x^2-xy+11x+11y=\\-x(x+y)+11(x+y)=\\-(x-11)(x+y)[/tex]
Answer:
(x - 11)(-x - y)
Step-by-step explanation:
To factor the polynomial 11x - xy + 11y - x² completely, let's group the terms and factor them separately.
Rearranging the terms, we have:
11x - xy + 11y - x²
Let's rearrange the terms again to group similar terms together:
x² + 11x - xy + 11y
Now, we can factor out the common factor from each pair of terms:
x(-x + 11) - y(x - 11)
Simplifying further, we can factor out -1 from the first pair of terms:
-x(x - 11) - y(x - 11)
Now, notice that we have a common factor of (x - 11) in both terms. Factoring out this common factor, we obtain:
(x - 11)(-x - y)
Therefore, the polynomial 11x - xy + 11y - x² can be factored completely as (x - 11)(-x - y).
Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of .
Answer:
The zero 1 has a multiplicity of 1.
The zero -2 has a multiplicity of 2.
Hope this clears up any confusion :)
Step-by-step explanation:
Answer:
The zero 1 has a multiplicity of 1.
The zero −2 has a multiplicity of 2 .
Step-by-step explanation:
In the figure below. MN is the arc of a circle with center L. If the length of arc MN is 6π, what is the area of sector LMN?
On a number line, the coordinates of X, Y, Z, and W are −7, −2, 2, and 7, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and
PLEASE ANSWER ASAP!!!
Fill in the box for the missing numerator in the set of equivalent expressions in the picture
Answer options are also shown in picture
any unrelated answer will be reported
Answer:
A. 14z - 28
Step-by-step explanation:
simplify z² - 3z
a. z(z - 3)
the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)
this means the numerator must also be multiplied by (z - 2)
14 x (z - 2) = 14z - 28
hope this helps :)
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are given below where x denotes seed density, and y denotes lawn quality.x 1 1 2 3 3 3 4 5y 30 40 40 40 50 65 50 50The sample linear correlation coefficient is r=0.600. At the 1% significance level, do the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated?
Answer:
I think it -1.50 to 10.58
Step-by-step explanation:
[09.01]
Identify the domain of the equation y=x2 - 6x + 1. (1 point)
Answer:
All real numbers.
Step-by-step explanation:
As there are no restrictions on the values of x, the domain is all real numbers.
Answer:
All real numbers.
Step-by-step explanation:
which function's graph has asymphotes located at the values x=+=n pi ? 1. y=csc x 2. y= cos x 3. y=tan x 4. y=cot x answer choices: A. 2 only B. 1 and 4 only C. 1 only D. 1 and 3 only please help!! ):
if 80% of 2 is 200.what is 70% of 27
Answer:
18.90
Hope i got it right
Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric receive (Disregard the $ sign when gridding your answer.)
Answer:
Abel receives $60, and Cedric receives $120
Step-by-step explanation:
Let Abel's share = A
Let Cedric's share = C
we are given the following
A + C = 180 - - - - - (1) (Abel and Cedric will share a total of $180)
[tex]A = \frac{C}{2}\ - - - - - - - (2)[/tex] (Abel will receive half as much as Cedric. )
from equation 2:
[tex]A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)[/tex]
putting this value of C in eqn (3) into eqn (1)
A + (2A) = 180
3A = 180
∴ A = 180 ÷ 3 = 60
to find C, let us replace the value of A in eqn (3) with 60
C = 2A - - - - (3)
C = 2 × 60
C = 120
Therefore, Abel receives $60, and Cedric receives $120
0 = -12 + 4y - 3x whats the slope
Answer:
3/4 is the slope
Step-by-step explanation:
We want to put this in slope intercept form
y = mx+b where m is the slope and b is the y intercept
0 = -12 + 4y - 3x
Subtract 4y from each side
-4y = -3x-12
Divide each side by -4
-4y/-4 = -3x/-4 -12/-4
y = 3/4 x +3
Answer:
Slope=3/4
Step-by-step explanation:
0=-12+4y-3x (Add 12 on the other side)
12=4y-3x (Add 3x on the other side)
3x+12=4y (Divide by 4)
y=3/4+3
1. The mean performance score on a physical fitness test for Division I student athletes is 947 with a population standard deviation of 205. Select a random sample of 64 of these students. Hint: we have a sample so use the standard error. What is the probability the mean of the sample is below 900
Answer:
0.033316
Step-by-step explanation:
We use the z score formula to solve for this question.
Since we are given the number of samples in the question, our z score formula is given as:
z = (x-μ)/ S.E
where x is the raw score
μ is the sample mean
S.E is the Standard error.
x is the raw score = 900
μ is the sample mean = Population mean = 947
Standard error =
This is calculated as Population standard deviation/ √No of samples
= 205/√64.
= 205/8
= 25.625
We proceed to calculate the z score
z = (x-μ)/ S.E
z = 900 - 947/25.625
= -1.83415
Using the z score table for normal distribution,
P(x≤ z) = P(z ≤ -1.83) = P(x ≤ 900)
P(x<900) = 0.033316
Therefore, the probability the mean of the sample is below 900 is 0.033316
The probability that a company will launch the product A and B are 0.45 and 0.60 respectively, in main while, probability that both products launched, is 0.35. what is the probability that Neither will of these products launch ? At least one product will be launched ?
Answer:
a) what is the probability that Neither will of these products launch ?
= 0.30
b) At least one product will be launched ?
= 0.70
Step-by-step explanation:
From the above question, we have the following information:
P(A) = 0.45
P(B) = 0.60
P(A ∩ B) = P(A and B) launching = 0.35
Step 1
We find the Probability that A or B will launch
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
a) what is the probability that Neither will of these products launch ?
1 - Probability ( A or B will launch)
= 1 - 0.70
= 0.30
b)At least one product will be launched?
This is equivalent to the probability that A or B will be launched
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
SAVINGS ACCOUNT Ms. Cole pays $2 a month
for online banking at her credit union. What is
the change in the balance of her account if she
pays this fee for 6 months?
Answer: $12 less.
Step-by-step explanation:
Given: Ms. Cole pays $2 a month for online banking at her credit union.
In 6 months she will pay = 6 x ($2)
= $12
It means that he balance will be decreased by $12 [as the amount was debited from the balance].
So, the change in the balance of her account if she pays this fee for 6 months = $12 less.
In a recent survey of 100 students, 34 said that they took a Math class as a freshman, 59 said that they took an English class as a freshman and 12 said they took both classes.
Required:
How many students took neither class as a freshman?
Answer:
19 studentsStep-by-step explanation:
We will use the set notation to solve this question.
let n(U) be the total number of students surveyed = 100
n(M) be the number of student that took math = 34
n(E) be the number of student that took English = 59
n(M∩E) be the number of student that took both classes= 12
n(M∪E)' be the number of student that took neither class = ?
Using the formula n(U) = n(M∪E) + n(M∪E)'
n(M∪E)' = n(U)-n(M∪E)
Before we can get the number of student that took neither class i.e n(M∪E)' we need to get n(M∪E).
n(M∪E) = n(M)+n(E)- n(M∩E)
n(M∪E) = 34+59-12
n(M∪E) = 81
Since n(M∪E)' = n(U)-n(M∪E);
n(M∪E)' = 100-81
n(M∪E)' = 19
Hence 19 students took neither class as a freshmen.
Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. Compare the two curves. The two curves will have ▼ the same line different lines of symmetry. The curve with the larger standard deviation will be ▼ more less spread out than the curve with the smaller standard deviation.
Answer:
The same mean ⇒ the same symmetry axis
Bigger standard deviation major spread
Step-by-step explanation: See Annex
The annex shows two different normal curves:
1.- N (μ₀ ; σ₁ )
2.- N (μ₀ ; σ₂ )
Where σ₁ > σ₂
They both have the same symmetry axis ( they have the same mean and both curves have to be symmetrically related to the mean )
Normal distribution curves spread symmetrically at both sides of the mean, but the wider curve is the one that has the bigger standard deviation. Standard deviation is a measure of the spread of the curve.
Whenever deviation is high, the data is more dispersed than when deviation is low.
Let the mean be 2.
Let the standard deviation be 0.3 for first graph. The data is more clustered around mean.
Let the standard deviation be 0.6 for second graph. The data is less clustered more dispersed from mean.
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Which choice shows the product of 22 and 49 ?
Answer:
1078
Step-by-step explanation:
The product of 22 and 49 is 1078.
Answer:
1078 is the product
Step-by-step explanation:
which best defines a service
Answer:
A service could be multiple things.
Step-by-step explanation:
Like, working as a scribe in a nursing home helping old people. Or, being part of a leadership club at school that funds food banks and things like that
Answer:
a
Step-by-step explanation:
X = y + 12
How to solve for variable
Answer:
x-y=12
Step-by-step explanation:
