# Fitchburg State University Statistics Questionnaire

Rev 06: Problem 1(1 point)

A box contains 10 red and 5 green balls. You randomly draw two balls, without replacement.

Find the probability of each possible outcome:

=

=

P(red, red)

P(red, green)

P(green, red)

P(green, green)

=

=

Now consider the following events:

.

C

G = the event the second ball is green

A = the event the balls are the same color

• D = the event the balls are different colors

=

=

=

=

P(G) =

P(A) =

P(D) =

P(A and G) =

P(A and D) =

P(A or G) =

=

=

Rev 06: Problem 2

(1 point)

100 college students on campus for the first time participate in a study of navigation strategies. Each student is given a map of campus, then told to find

their way to a specific location however they choose. The researchers then observe whether the students check the map or ask directions first. 36 female

students asked directions first and 21 checked the map first. 14 male students asked directions and 29 checked the map first.

Suppose one of these students is selected randomly, and consider the following events:

F = the student is female

M = the student is male

А. = the student asked directions first

C = the student checked the map first

A

C

Total

F

M

Total

What is the chance that the chosen student is male?

What is the probability that the chosen student is male or asked directions first?

What is the probability that the chosen student is male and asked directions first?

What is the probability that the chosen student checked the map first, given you know the student is female?

Rev 07: Problem 1

(1 point)

If a student guesses randomly on a 5-question multiple-choice quiz, the following table gives the probability distribution of the discrete random variable,

X = number of correct guesses.

=

P(X = 2)

0.2373

0

1

0.3955

2

0.2637

3

0.0879

4

0.0146

5

0.0010

Translate to probability notation, then find the probability:

Use , and != for #, as needed.

7

Find the probability of O correct guesses.

Find the probability of at least 3 correct guesses.

II

Find the probability of at most 2 correct guesses.

II

=

How many correct guesses are expected?

Rev 07: Problem 2

(1 point)

=

A box contains 200 balls: 175 are red, 20 are orange, 4 are blue, and 1 is green. One ball is pulled from the box at random. If it is red, you lose $2. If it is

orange, you win $4. If it is blue, you win $17. If it is green, you win $170. Let X = the amount you win, in dollars (so X is negative if you lose). Complete

the PDF

Note:

• Column labels go in the first row.

• The x-values must be in ascending order.

Over the long run of playing this game, what are your expected average winnings per game? $

Rev 08: Problem 1

(1 point)

Trains on the Silver line leave High St. Station every 15 minutes. Silver line trains take 19 minutes to get to the airport once they leave the station. Let X =

the time from a passenger’s arrival at the station to his or her arrival at the airport. We know X is uniformly distributed from 19 to 34 minutes.

a. What is the chance a Silver-line passenger will get to the airport in 24 to 28 minutes?

b. What percent of Silver-line passengers will get to the airport in under 24 minutes?

c. What percent of passengers take more than 28 minutes to get to the airport?

d. How long should a passenger expect it to take to get to the airport from his/her arrival at the station?

minutes

e. What time to the airport is the 80th percentile?

minutes

f. The middle 80% of times are between

and

minutes.

Rev 06: Problem 1

(1 point)

A box contains 10 red and 5 green balls. You randomly draw two balls, without replacement.

Find the probability of each possible outcome:

=

=

P(red, red)

P(red, green)

P(green, red)

P(green, green)

=

=

Now consider the following events:

.

C

G = the event the second ball is green

A = the event the balls are the same color

• D = the event the balls are different colors

=

=

=

=

P(G) =

P(A) =

P(D) =

P(A and G) =

P(A and D) =

P(A or G) =

=

=

Rev 06: Problem 2

(1 point)

100 college students on campus for the first time participate in a study of navigation strategies. Each student is given a map of campus, then told to find

their way to a specific location however they choose. The researchers then observe whether the students check the map or ask directions first. 36 female

students asked directions first and 21 checked the map first. 14 male students asked directions and 29 checked the map first.

Suppose one of these students is selected randomly, and consider the following events:

F = the student is female

M = the student is male

А. = the student asked directions first

C = the student checked the map first

A

C

Total

F

M

Total

What is the chance that the chosen student is male?

What is the probability that the chosen student is male or asked directions first?

What is the probability that the chosen student is male and asked directions first?

What is the probability that the chosen student checked the map first, given you know the student is female?

Rev 07: Problem 1

(1 point)

If a student guesses randomly on a 5-question multiple-choice quiz, the following table gives the probability distribution of the discrete random variable,

X = number of correct guesses.

=

P(X = 2)

0.2373

0

1

0.3955

2

0.2637

3

0.0879

4

0.0146

5

0.0010

Translate to probability notation, then find the probability:

Use , and != for #, as needed.

7

Find the probability of O correct guesses.

Find the probability of at least 3 correct guesses.

II

Find the probability of at most 2 correct guesses.

II

=

How many correct guesses are expected?

Rev 07: Problem 2

(1 point)

=

A box contains 200 balls: 175 are red, 20 are orange, 4 are blue, and 1 is green. One ball is pulled from the box at random. If it is red, you lose $2. If it is

orange, you win $4. If it is blue, you win $17. If it is green, you win $170. Let X = the amount you win, in dollars (so X is negative if you lose). Complete

the PDF

Note:

• Column labels go in the first row.

• The x-values must be in ascending order.

Over the long run of playing this game, what are your expected average winnings per game? $

Rev 08: Problem 1

(1 point)

Trains on the Silver line leave High St. Station every 15 minutes. Silver line trains take 19 minutes to get to the airport once they leave the station. Let X =

the time from a passenger’s arrival at the station to his or her arrival at the airport. We know X is uniformly distributed from 19 to 34 minutes.

a. What is the chance a Silver-line passenger will get to the airport in 24 to 28 minutes?

b. What percent of Silver-line passengers will get to the airport in under 24 minutes?

c. What percent of passengers take more than 28 minutes to get to the airport?

d. How long should a passenger expect it to take to get to the airport from his/her arrival at the station?

minutes

e. What time to the airport is the 80th percentile?

minutes

f. The middle 80% of times are between

and

minutes.

Rev 09: Problem 1

(1 point)

Scores on the Final exam for Precalculus are normally distributed with a mean of 73.3 and a standard deviation of 7.7. Use the Standard Normal

Probability and the Inverse Normal tables to answer the questions.

a. If we choose a Precalculus student at random, what is the probability that his or her Final exam score is over 83?

b. What percent of the exam scores are between 70 and 80?

c. What is the minimum exam score (to the nearest 0.1) to be in the top 1%?

d. The middle 60% of exam scores (to the nearest 0.1) are between

and

Rev 10: Problem 1

(1 point)

At Mythic U, 17% of students have green eyes. Use the Standard Normal Probability and the Inverse Normal tables to answer the questions. (Answers

should be to the nearest 0.1%)

a. With a sample size of 700, the middle 90% of samples will have sample proportions between

and

b. With a sample size of 1150, the middle 90% of samples will have sample proportions between

and

Note: You can earn partial credit on this problem.

Rev 10: Problem 2

(1 point)

Scores on the SAT mathematics exam are normally distributed with a mean of 506 and a standard deviation of 102 (Use the Standard Normal Probability

and the Inverse Normal tables to answer the questions.)

a. If we collect a random sample of 28 SAT mathematics scores, what is the probability that the mean score will be less than 492?

b. With a sample size of 28, the middle 80% of random samples of SAT mathematics scores will have sample means (to the nearest 0.1) between

and

=

=

=

P(G) = 0.3333

P(A) = 0.5238

P(D) = 0.4762

P(A and G) = 0.0952

P(A and D) = 0.0000

P(A or G) = 1.0000

=

At least one of the answers above is NOT correct.

Scores on the Final exam for Precalculus are normally distributed with a mean of 73.3 and a standard deviation of 7.7. Use the Standard Normal

Probability and the Inverse Normal tables to answer the questions.

a. If we choose a Precalculus student at random, what is the probability that his or her Final exam score is over 83? 0.103

b. What percent of the exam scores are between 70 and 80? 47.38

c. What is the minimum exam score (to the nearest 0.1) to be in the top 1%? 91.2

d. The middle 60% of exam scores (to the nearest 0.1) are between

66.8

and

79.8

Results for this submission

Entered

Answer Preview

Result

Message

0.1038

0.1038

correct

47.38%%

incorrect

Can’t take percent of a percent

91.2

91.2

correct

66.8

66.8

correct

79.8

79.8

correct

At least one of the answers above is NOT correct.

Scores on the Final exam for Precalculus are normally distributed with a mean of 73.3 and a standard deviation of 7.7. Use the Standard Normal

Probability and the Inverse Normal tables to answer the questions.

a. If we choose a Precalculus student at random, what is the probability that his or her Final exam score is over 83? 0.103

b. What percent of the exam scores are between 70 and 80? 47.38

c. What is the minimum exam score (to the nearest 0.1) to be in the top 1%? 91.2

d. The middle 60% of exam scores (to the nearest 0.1) are between

66.8

and 79.8

Rev 09: Problem 1

(1 point)

Scores on the Final exam for Precalculus are normally distributed with a mean of 71.9 and a standard deviation of 7.2. Use the Standard Normal

Probability and the Inverse Normal tables to answer the questions.

a. If we choose a Precalculus student at random, what is the probability that his or her Final exam score is over 83?

b. What percent of the exam scores are between 70 and 80?

c. What is the minimum exam score (to the nearest 0.1) to be in the top 4%?

d. The middle 60% of exam scores (to the nearest 0.1) are between

and

Quiz 9

TU

You will see Quiz 9 assigned in WebWork. It will appear as Take Q9 test.

Notes

• WebWork expects you to get your probabilities and percentile z-scores from the tables posted here on Blackboard. It is possible to use RStudio or some calculators to get

better answers, but WebWork won’t recognize those as correct.

Remember, if you calculate a probability as a decimal, you need to round to 4 decimal places. If you give the answer as a percent, your percent should have 2 decimal

places.

Rev 10: Problem 1

(1 point)

At Mythic U, 17% of students have green eyes. Use the Standard Normal Probability and the Inverse Normal tables to answer the questions. (Answers

should be to the nearest 0.1%)

a. With a sample size of 700, the middle 90% of samples will have sample proportions between

16.1% and

17.99

b. With a sample size of 1150, the middle 90% of samples will have sample proportions between

16.3% and 17.7%

Rev 10: Problem 2

(1 point)

Results for this submission

Entered

Answer Preview

Result

0.2338

0.2338

incorrect

481.3

481.3

correct

530.7

530.7

correct

At least one of the answers above is NOT correct.

Scores on the SAT mathematics exam are normally distributed with a mean of 506 and a standard deviation of 102 (Use the Standard Normal Probability

and the Inverse Normal tables to answer the questions.)

a. If we collect a random sample of 28 SAT mathematics scores, what is the probability that the mean score will be less than 492? 0.233

b. With a sample size of 28, the middle 80% of random samples of SAT mathematics scores will have sample means (to the nearest 0.1) between

481.3 and 530.7

Rev 10: Problem 1

(1 point)

At Mythic U, 17% of students have green eyes. Use the Standard Normal Probability and the Inverse Normal tables to answer the questions. (Answers

should be to the nearest 0.1%)

a. With a sample size of 700, the middle 90% of samples will have sample proportions between

16.1% and

17.99

b. With a sample size of 1150, the middle 90% of samples will have sample proportions between

16.3% and 17.7%