callen37@jeffersonstate.edu ()

CH-7 (Homework)

Instructor
Konstantinos Theodorou
Jefferson State CC, AL

Current Score

QuestionPoints
1

1/3

2

3/3

Check mark
3

0/4

4

2/2

Check mark
5

2/10

6

1/1

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7

–/1

8

–/1

9

0/1

10

2/2

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11

1/2

12

1/2

13

1/1

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14

1/1

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15

2/2

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16

2/2

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17

–/3

18

2/3

19

–/2

20

9/9

Check mark
21

2/3

22

1/4

Total Score

Due Date

Sun, Dec 13, 202011:59 PM CST

Assignment Submission & Scoring

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1.

[1/3 Points]BBBasicStat8 7.1.002.MI.
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1/3
 
Look at the normal curve below, and find 𝜇, 𝜇 + 𝜎, and 𝜎.
𝜇 = Incorrect: Your answer is incorrect.
𝜇 + 𝜎 = Incorrect: Your answer is incorrect.
𝜎 = Correct: Your answer is correct.
WebAssign Plot

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2.

[3/3 Points]BBBasicStat8 7.1.003.
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1/1 1/1 1/1
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3/3
 
Look at the two normal curves in the figures below.
Which has the larger standard deviation?
     Correct: Your answer is correct.

What is the mean of the curve in Figure (a)?
Correct: Your answer is correct.

What is the mean of the curve in Figure (b)?
Correct: Your answer is correct.

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3.

[0/4 Points]BBBasicStat8 7.1.007.
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0/4
 
Assuming that the heights of college women are normally distributed with mean 61 inches and standard deviation 3.0 inches, answer the following questions. (Hint: Use the figure below with mean 𝜇 and standard deviation 𝜎.)
(a) What percentage of women are taller than 61 inches?
Incorrect: Your answer is incorrect. %

(b) What percentage of women are shorter than 61 inches?
Incorrect: Your answer is incorrect. %

(c) What percentage of women are between 58.0 inches and 64.0 inches?
%

(d) What percentage of women are between 55.0 and 67.0 inches?
%

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4.

[2/2 Points]BBBasicStat8 7.2.004.
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2/2
 
What are the values of the mean and standard deviation of a standard normal distribution?
𝜇 = Correct: Your answer is correct.
𝜎 = Correct: Your answer is correct.

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5.

[2/10 Points]BBBasicStat8 7.2.010.
Question Part
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1 2 3 4 5 6 7 8 9 10
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2/10
 
Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean 𝜇 = 28.1 kilograms and standard deviation 𝜎 = 3.3 kilograms. Let x be the weight of a fawn in kilograms.
Convert the following x intervals to z intervals. (Round your answers to two decimal places.)
(a)    x < 30
z <

(b)    19 < x
< z

(c)    32 < x < 35
< z <

Convert the following z intervals to x intervals. (Round your answers to one decimal place.)
(d)    −2.17 < z
< x

(e)    z < 1.28
x <

(f)    −1.99 < z < 1.44
< x <
(g) If a fawn weighs 14 kilograms, would you say it is an unusually small animal? Explain using z values and the figure above.
     Correct: Your answer is correct.

(h) If a fawn is unusually large, would you say that the z value for the weight of the fawn will be close to 0, −2, or 3? Explain.
     Correct: Your answer is correct.

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6.

[1/1 Points]BBBasicStat8 7.2.020.S.
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1/1
 
Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
The area to the right of z = 0.08 is Correct: Your answer is correct. .

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7.

[–/1 Points]BBBasicStat8 7.2.018.S.
Question Part
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1
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–/1
 
Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
The area to the left of z = 0.65 is .

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8.

[–/1 Points]BBBasicStat8 7.2.024.S.
Question Part
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1
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–/1
 
Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
The area between z = 0 and
z = −1.97
 is .

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9.

[0/1 Points]BBBasicStat8 7.2.028.S.
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1
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0/1
 
Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
The area between
z = 1.33
 and z = 2.25 is Incorrect: Your answer is incorrect. .

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10.

[2/2 Points]BBBasicStat8 7.2.033.MI.S.
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Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
P(z ≤ −0.24)
 = Correct: Your answer is correct.

Shade the corresponding area under the standard normal curve.

Correct: Your answer is correct.

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11.

[1/2 Points]BBBasicStat8 7.2.037.MI.S.
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Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
P(z ≥ 1.44) =

Shade the corresponding area under the standard normal curve.

Correct: Your answer is correct.

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12.

[1/2 Points]BBBasicStat8 7.2.041.MI.S.
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Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
P(−1.24 ≤ z ≤ 2.63)
 =

Shade the corresponding area under the standard normal curve.

Correct: Your answer is correct.

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13.

[1/1 Points]BBBasicStat8 7.3.005.MI.S.
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1/1
 
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
𝜇 = 4; 𝜎 = 6
P(1 ≤ x ≤ 13) = Correct: Your answer is correct.

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14.

[1/1 Points]BBBasicStat8 7.3.012.S.
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Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
𝜇 = 101; 𝜎 = 17
P(x ≥ 120) = Correct: Your answer is correct.

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15.

[2/2 Points]BBBasicStat8 7.3.015.MI.S.
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Find z such that 5% of the standard normal curve lies to the left of z. (Round your answer to three decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
z = Correct: Your answer is correct.

Sketch the area described.

Correct: Your answer is correct.

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16.

[2/2 Points]BBBasicStat8 7.3.016.S.
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Find z such that 2.9% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
z = Correct: Your answer is correct.

Sketch the area described.

Correct: Your answer is correct.

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17.

[–/3 Points]BBBasicStat8 7.3.028.MI.S.
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Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 7.2 minutes and a standard deviation of 2.1 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
(a) the response time is between 3 and 9 minutes


(b) the response time is less than 3 minutes


(c) the response time is more than 9 minutes

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18.

[2/3 Points]BBBasicStat8 7.5.008.MI.
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2/3
 
Suppose x has a distribution with 𝜇 = 74 and 𝜎 = 8.
A button hyperlink to the SALT program that reads: Use SALT.
(a)
If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?
     Correct: Your answer is correct.
(b)
If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?
     Correct: Your answer is correct.
Find P(70 ≤ x ≤ 75). (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.

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19.

[–/2 Points]BBBasicStat8 7.5.010.MI.
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Consider an x distribution with standard deviation 𝜎 = 40.
(a) If specifications for a research project require the standard error of the corresponding x distribution to be 2, how large does the sample size need to be?
n =

(b) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?
n =

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20.

[9/9 Points]BBBasicStat8 7.5.011.S.
Question Part
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9/9
 
Suppose x has a distribution with 𝜇 = 13 and 𝜎 = 7.
A button hyperlink to the SALT program that reads: Use SALT.
(a) If a random sample of size n = 43 is drawn, find 𝜇x, 𝜎 x and P(13 ≤ x ≤ 15). (Round 𝜎x to two decimal places and the probability to four decimal places.)
𝜇x = Correct: Your answer is correct.
𝜎 x = Correct: Your answer is correct.
P(13 ≤ x ≤ 15) = Correct: Your answer is correct.

(b) If a random sample of size n = 58 is drawn, find 𝜇x, 𝜎 x and P(13 ≤ x ≤ 15). (Round 𝜎 x to two decimal places and the probability to four decimal places.)
𝜇x = Correct: Your answer is correct.
𝜎 x = Correct: Your answer is correct.
P(13 ≤ x ≤ 15) = Correct: Your answer is correct.

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is Correct: Your answer is correct. part (a) because of the Correct: Your answer is correct. sample size. Therefore, the distribution about 𝜇x is Correct: Your answer is correct. .

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21.

[2/3 Points]BBBasicStat8 7.5.014.S.
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Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)
Correct: Your answer is correct.

(b) If a random sample of twenty-one 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
     Correct: Your answer is correct.

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22.

[1/4 Points]BBBasicStat8 7.6.009.MI.S.
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1/4
 
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 761 high school seniors, find the following probabilities. (Round your answers to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
(a) 15 or more will live beyond their 90th birthday
Correct: Your answer is correct.

(b) 30 or more will live beyond their 90th birthday
Incorrect: Your answer is incorrect.

(c) between 25 and 35 will live beyond their 90th birthday
Incorrect: Your answer is incorrect.

(d) more than 40 will live beyond their 90th birthday
Incorrect: Your answer is incorrect.

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