2 CORRECTIONS

11/17/21, 7:31 PM Lyana Gomez's Quiz History: Exam 2 (11/03/2021) (Remotely Proctored)

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Exam 2 (11/03/2021) (Remotely Proctored) Results for Lyana Gomez

Score for this quiz: 29 out of 111 Submitted Nov 3 at 8:10pm This attempt took 117 minutes.

3.5 / 15 ptsQuestion 1

The following data represent the ideal number of children for a random sample of 900 adult Americans

x 0 1 2 3 4 5

Frequency 15 30 260 500 85 10

a. The above is a frequency distribution for the random variable X. Construct a probability distribution for the random variable X by filling in the table below. Round each probability to 4 decimal places (4 points)

x P(x)

0 0.0167

1 0.3333

2 0.3999

3 0.6666

4 0.0944

5 0.0111

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Answer 1:

Answer 2:

Answer 3:

b. Based on your probability distribution from part a, what is the probability that a randomly selected adult would want at least 1 child? (4 points)

P( ) = 3

c. What is the probability that 5 randomly selected adults all want at least 1 child? [HINT: Use your answer from part b] (3 pts)

15

d. Based on your probability distribution from part a, What are the mean and standard deviation for ideal number of children in a family (round both to 4 decimal places)? (4 points) [HINT: Remember that this is a discrete distribution]

Mean = 2.3410

standard deviation = 0.9570

𝑥 ≥ 1

0.0167Correct!Correct!

.0167 orrect Answerorrect Answer

0.3333ou Answeredou Answered

.0333 orrect Answerorrect Answer

0.0333 orrect Answerorrect Answer

0.3999ou Answeredou Answered

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Answer 4:

Answer 5:

Answer 6:

Answer 7:

Answer 8:

Answer 9:

.2889 orrect Answerorrect Answer

0.2889 orrect Answerorrect Answer

0.6666ou Answeredou Answered

.5556 orrect Answerorrect Answer

0.5556 orrect Answerorrect Answer

0.0944Correct!Correct!

.0944 orrect Answerorrect Answer

0.0111ou Answeredou Answered

0.0165 orrect Answerorrect Answer

.0165 orrect Answerorrect Answer

3ou Answeredou Answered

.9833 orrect Answerorrect Answer

.9833 orrect Answerorrect Answer

15ou Answeredou Answered

.9192 orrect Answerorrect Answer

0..9192 orrect Answerorrect Answer

11/17/21, 7:31 PM Lyana Gomez's Quiz History: Exam 2 (11/03/2021) (Remotely Proctored)

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Answer 10:

2.3410ou Answeredou Answered

2.7111 orrect Answerorrect Answer

0.9570ou Answeredou Answered

0.7922 orrect Answerorrect Answer

.7922 orrect Answerorrect Answer

Teacher's correction: For part a, P(5) = 0.0111 . Some of the other probabilities are incorrect thought (-1.5 pts) b/c) incorrect (- 7 pts) d) incorrect (-3 pts)

10 / 23 ptsQuestion 2

The average height of U.S. women is approximately normally distributed, with a mean of 64.5 inches and standard deviation of 2.5 inches. (4 + 4 + 3 + 2 + 4 + 2 + 4 = 23 points total)

Round all probabilities to 4 decimal places.

a) What is the probability that a randomly selected woman's height is 66 inches or less? Show work/calculator input and write a conclusion sentence (does not need to be an interpretation).

b) What is the probability that a randomly selected woman's height is 62 inches or more? Show work/calculator input (No conclusion sentence necessary).

c) What is the probability that a randomly selected woman's height is between 60 and 69 inches, inclusive? Show work/calculator input and

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Your Answer:

write a conclusion sentence (does not need to be an interpretation).

d) If we were to randomly sample 600 women, how many women would we expect to have a height of 66 inches or less? (HINT: Use your work in part a). Round to a whole number.

[HINT: Do not answer part d as a proportion. So if for example your answer was 300 out of the 600 women, your answer should be "300 women", not 300/600 = "0.5 women"]

Show work/calculator input (No conclusion sentence necessary).

e) The 20% shortest women are shorter than what height? In other words find P (Round your answer UP to the nearest whole number). Show work/calculator input and write a conclusion sentence (does not need to be an interpretation).

f) If we were to take a sample of 36 women, is the sampling distribution of the sample mean normally distributed? How would you know?

g) If we were to take a sample of 36 women, what is the probability that the mean height of this sample was 65 inches or less? Show work/calculator input and write a conclusion sentence (does not need to be an interpretation).

20

A. P(X ≤ =66) = 0.7367 B. P(X≥ =62 ) = 0.8413 C. P( 60 ≤X≤ 69) = 0.9381

a) incorrect (-1 pt) d/e/f/g) Missing (-12 pts)

6 / 16 ptsQuestion 3

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It is estimated that 80% of all dogs in the U.S. are spayed or neutered. Suppose we randomly sample 40 dogs. (use Binomial distribution, NOT normal approximation) (4 points each):

Round to 4 decimal places

a. Find the probability that exactly 33 out of 40 dogs is spayed or neutered.

Probability 0.2512

StatCrunch/Calculator Function and/or Input (or show work):

b. What is the probability that at least 29 out of 40 dogs is spayed or neutered?

Probability

StatCrunch/Calculator Function and/or Input:

(or show work)

c. What is the probability that between 17 and 26 out of 40 dogs is spayed or neutered?

Probability 0.0294

StatCrunch/Calculator Function and/or Input:

(or show work)

d. What are the mean and standard deviation for the number of dogs who are spayed or neutered out of this sample of 40 dogs? (Round to four decimal places, if necessary). Include any work/calculator functions.

P(X = 33 ) = 0.25

P( 17 ≤X≤ 26 ) =

11/17/21, 7:31 PM Lyana Gomez's Quiz History: Exam 2 (11/03/2021) (Remotely Proctored)

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Answer 1:

Answer 2:

Answer 3:

Answer 4:

𝜇=

𝜎=

0.2512ou Answeredou Answered

0.1512 orrect Answerorrect Answer

.1512 orrect Answerorrect Answer

P(X = 33 ) = 0.2512ou Answeredou Answered

Binomial( n = 40, p = .80 , x = 33 ) orrect Answerorrect Answer

binomial( n = 40, p = .80 , x = 33 ) orrect Answerorrect Answer

binomial( n = 40, p = .8 , x = 33 ) orrect Answerorrect Answer

Binomial( n = 40, p = .8 , x = 33 ) orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

0.9125 orrect Answerorrect Answer

.9125 orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

Binomial( n = 40, p = .8 , x>=29 ) orrect Answerorrect Answer

binomial( n = 40, p = .8 , x>=29 ) orrect Answerorrect Answer

Binomial( n = 40, p = .80 , x>=29 ) orrect Answerorrect Answer

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Answer 5:

Answer 6:

Answer 7:

Answer 8:

Binomial( n = 40, p = .80 , x>=29 ) orrect Answerorrect Answer

0.0294ou Answeredou Answered

0.0194 orrect Answerorrect Answer

.0194 orrect Answerorrect Answer

P( 17 ≤X≤ 26 ) = 0.0294ou Answeredou Answered

Binomial( n = 40, p = .80 , 17 <= x <= 26 ) orrect Answerorrect Answer

binomial( n = 40, p = .80 , 17 <= x <= 26 ) orrect Answerorrect Answer

Binomial( n = 40, p = .8 , 17 <= x <= 26 ) orrect Answerorrect Answer

binomial( n = 40, p = .8 , 17 <= x <= 26 ) orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

32 orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

2.5298 orrect Answerorrect Answer

a/c) both off by .1 or .01, not sure why? (-2 pts) b/d) missing (-8 pts)

8 / 18 ptsQuestion 4

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A guidance counselor at a middle school collected the following information regarding the employment status of married couples within his school's boundaries, specifically recording which member of the couple is working (The older spouse only, younger spouse only, or both spouses).

Number of Children 18 Years or Younger

WORKED 0 1 2 or more

Older Spouse

172 79 174 42

Younger Spouse

94 17 15 12

Both Spouses

522 757 370 16

Total 788 853 559 22

a. Fill in the totals in the table above (2 points).

For parts b. through e. , round to 4 decimal places

b. What is the probability that, for a married couple selected at random, both spouses work? (4 points) [Feel free to include work]

0.1682

c. What is the probability that, for a married couple selected at random, the couple has no children or only the older spouse works? (4 points) [Feel free to include work]

0.0782

d. What is the probability that, for a married couple selected at random, the couple has 1 child under the age of 18 and only the older spouse

works? (4 points) [Feel free to include work]

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Answer 1:

Answer 2:

Answer 3:

Answer 4:

Answer 5:

Answer 6:

Answer 7:

Answer 8:

0.0359

e. What is the probability that for a married couple with no kids, that both spouses work? (4 points) [Feel free to include work]

0.2372

425Correct!Correct!

126Correct!Correct!

1649Correct!Correct!

788Correct!Correct!

853Correct!Correct!

559Correct!Correct!

2200Correct!Correct!

0.1682ou Answeredou Answered

0.2372 orrect Answerorrect Answer

.2372 orrect Answerorrect Answer

11/17/21, 7:31 PM Lyana Gomez's Quiz History: Exam 2 (11/03/2021) (Remotely Proctored)

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Answer 9:

Answer 10:

Answer 11:

522/2200 = .2372 orrect Answerorrect Answer

522/2200 = 0.2372 orrect Answerorrect Answer

0.0782ou Answeredou Answered

.4732 orrect Answerorrect Answer

0.4732 orrect Answerorrect Answer

(788 + 425 - 172)/2200 = 0.4732 orrect Answerorrect Answer

(788 + 425 - 172)/2200 = .4732 orrect Answerorrect Answer

0.0359Correct!Correct!

79/2200 = .0359 orrect Answerorrect Answer

79/2200 = 0.0359 orrect Answerorrect Answer

.0359 orrect Answerorrect Answer

0.2372ou Answeredou Answered

.6624 orrect Answerorrect Answer

0.6624 orrect Answerorrect Answer

522/788 = 0.6624 orrect Answerorrect Answer

522/788 = .6624 orrect Answerorrect Answer

NOTE: Answer for b should have been 1649/22000 = 0.7495 b/c) incorrect, no work to give partial credit to (-8 pts) e) incorrect (-2 pts)

11/17/21, 7:31 PM Lyana Gomez's Quiz History: Exam 2 (11/03/2021) (Remotely Proctored)

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0 / 10 ptsQuestion 5

Answer 1:

UnansweredUnanswered

7. According to CTIA, 41% of all U.S. households are wireless-only households.

(You can show work if you want, it may score you some partial credit points)

Round all answers to 4 decimal places, if necessary.

a. In a simple random sample of 200 households, determine the mean and standard deviation number of wireless only households. (Hint: What kind of distribution is this?) (4 points)

𝝁 =

𝝈=

b. In a simple random sample of 200 households, researchers found that less than 95 of the households were wireless only. Is this result unusual? What if it were less than 65 households? Show your work. [A result is unusual if it is more than two standard deviations from the mean] (6 points)

Less than 95 households would be Unusual or Not Unusual?

=

Less than 65 households would be Unusual or Not Unusual?

𝑃 (𝑋 < 95) =

𝑃 (𝑋 < 65)

(You left this blank)ou Answeredou Answered

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Answer 2:

Answer 3:

Answer 4:

Answer 5:

Answer 6:

82 orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

6.9556 orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

0.9632 orrect Answerorrect Answer

.9632 orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

Not unusual orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

.0055 orrect Answerorrect Answer

0.0055 orrect Answerorrect Answer

0.0003 orrect Answerorrect Answer

.0003 orrect Answerorrect Answer

(You left this blank)ou Answeredou Answered

Unusual orrect Answerorrect Answer

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a. mean = np = .41(200) = 82

standard deviation = = 6.9556

b. Use Stats --> Calculators --> Binomial

Binomial(n = 200, p = 0.41, X < 95) = 0.9632

0.9632 > 0.05, so less than 95 households would NOT be unusual.

Binomial(n = 200, p = 0.41, X < 65) = 0.0055

0.0055 < 0.05, so less than 65 households would be unusual.

=𝑛𝑝 (1 − 𝑝)‾ ‾‾‾‾‾‾‾‾√ (200) (.41) (.59)‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

0 / 14 ptsQuestion 6UnansweredUnanswered

As of 2020, approximately 18 percent of the U.S. residents was covered by Medicare.

(Use Ch 8.2 techniques, do NOT use Ch6.2/Binomial Distribution tools).

a. Suppose we sample 120 members of the U.S. residents, and find the proportion covered by Medicare. Verify that the sampling distribution of the sample proportion �̂� is normally distributed. (2 points)

b. Find the (i) mean μ of the samping distribution of �̂� and (ii) standard deviation σ of the sampling distribution of �̂� for the sample proportion of U.S. population covered by Medicare. If necessary, round either answer (or both) to 6 decimal places (4 points)

Mean = _____

Standard deviation = _____

𝑝̂

𝑝̂

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Your Answer:

c. From the sample of 120 US. residents, calculate the probability that the sample proportion �̂� is less than 0.17. In other words, find 𝑃(𝑝̂ < 0.17). Include work/technology input, and write a conclusion sentence to indicate what this probability represents in this situation. Round to 4 decimal places. (4 points)

d. From the sample of 120 U.S., calculate the probability that between 17.5% and 19% of them are covered by Medicare. Include work/technology input, and write a conclusion sentence to indicate what this probability represents in this situation. Round to 4 decimal places (4 points)

1.5 / 6 ptsQuestion 7

z-scores follow a standard normal distribution, meaning they are normally distributed with a mean of 0 and standard deviation of 1. (3 points each)

a. If P(-b < z < b) = .7555 (edit: you may also use 0.755) what is the value for b and -b? Round to 4 decimal places.

b = 1.2636

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Answer 1:

Answer 2:

Answer 3:

-b = -1.2636

b. If the proportion of z-scores above b is 0.1788, what is b? In other words, if P(z > b ) = 0.1788, what is the value for b? Round to 4 decimal places.

b = 0.4390

1.2636ou Answeredou Answered

1.1626 orrect Answerorrect Answer

1.1638 orrect Answerorrect Answer

-1.2636ou Answeredou Answered

-1.1626 orrect Answerorrect Answer

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0.4390ou Answeredou Answered

0.9199 orrect Answerorrect Answer

.9199 orrect Answerorrect Answer

Teacher's note: For part a, 1.1638 and -1.1638 are also valid answers a) answers off not, not sure why (-1.5 pts) b) incorrect (-3 pts)

0 / 12 ptsQuestion 8

Your Answer:

UnansweredUnanswered

According to the U.S Census bureau's most recent data, 42% of all U.S. adults age 25 or older hold an associate's degree or higher (4 points each). SHOW WORK. Round all probabilities to 4 decimal places.

a. If we were to randomly select six U.S. adults age 25 or older, find the probability that all six hold an associate's degree or higher. Write a conclusion sentence.

b. If we were to randomly select four U.S. adults age 25 or older are randomly selected, find the probability that none of them hold an associate's degree or higher? Write a conclusion sentence.

c. If four U.S. adults age 25 or older are randomly selected, what is the probability that at least one of them holds an associate's degree or higher? Write a conclusion sentence. Is this result unusual? [An event is unusual if it's probability is less than 0.05]

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Ch 8

- Sampling distribution of of 𝑥̅ is normally distributed if OR the population from which you are sampling is normally distributed.

- The sampling distribution of �̂� is normally distributed if np(1-p) is greater than or equal to 10.

StatCrunch

Discrete Distribution: Stat --> Calculators --> Custom

Binomial Distribution: Stat --> Calculators --> Binomial

Normal Distribution: Stat --> Calculators --> Normal

𝑛 ≥ 30

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Quiz Score: 29 out of 111

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