1) Consider the following data set consisting of test scores of students in a math class:

5 16 18 51 59 59 62 63 64

65 66 66 67 69 70 71 72 73

74 75 76 76 76 77 83 83 85

a. Obtain the five-number summary (i.e., Min,Q

1

Q1

,Q

2

=

Q2=

median,Q

3

Q3

, Max) for the data

b. Calculate the lower and upper fences.

Lower fence:

Upper fence:

c. Check for any outliers using fences. List the outliers separated by commas. If there are no outliers, type "DNE."

d. draw box plot and make sure to indicate the fences and any outliers. Upload your work below.

e. For this frequency distribution, which measure of the center is larger, the median or the mean? (You do not have to calculate the mean to answer this question).

• median = mean
• mean
• median

f. TheSelect an answer

mean

median

better describes the center of the data because the shape of this distribution isSelect an answer

symmetric

skewed-right

skewed-left

.

g. Complete the following sentence.

The test score does not exceedfor 75% of the students in this class.

h. Complete the following sentence.

The test score is at leastfor 75% of the students in this class.

2) A regression was run to determine if for a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related. The results were:

y^= a+bx

a=-0.4875

b=2.94

For this baseball season, the lowest on-base percentage was 0.310 and the highest was 0.362.

(a) Write the equation of the Least Square Regression line.

(b) Which is a possible value for the correlation coefficient, r?

• 0.72
• -1.143
• 1.235
• -0.68

(c) What does the slope mean in the context of this problem?

(d) As the on-base percentage increases by 5 percent, the predicted winning percentageSelect an answer

increases

decreases

bypercent.

(e) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage is 0.156? Why or why not?

(f) Based on this model, what would you expect the winning percentage to be for a team with on-base percentage 0.35? (Round your answer to three decimal places.)

3) 500 children ages 5-11 were asked the following question:

"Do you read books for fun every day?"

Results are shown in the two-way table below.

BoyGirlTotalYes4373No187197Total500

a. In this sample, what proportion of children are boys? (Round your answer to the nearest hundredth)

b. What proportion of boys read books for fun every day? (Round your answer to the nearest hundredth)

c. What proportion of girls read books for fun every day? (Round your answer to the nearest hundredth)

d. Based on the findings, does the likelihood of reading books for fun depend on the gender of a child? Explain.

e. If a child is selected at random, find the probability that the child reads book for fun. (Round your answer to the nearest hundredth)

f. If a child is selected at random, find the probability that the child is a girl AND reads book for fun. (Round your answer to the nearest hundredth)

g. If a child is selected at random, find the probability that the child is a girl OR reads book for fun. (Round your answer to the nearest hundredth)

h. If a child is selected at random, find the probability that the child reads book for fun GIVEN that the child is a girl. (Round your answer to the nearest hundredth)

4) Suppose you play a die-rolling game in which a fair 6-sided die is rolled once. If the outcome of the roll (the number of dots on the side facing upward) is odd, you win as many dollars as the number you have rolled. Otherwise, you lose as many dollars as the number you have rolled. LetX

X

be the profit of the game or the amount of money won or lost per roll. Negative profit corresponds to lost money.

(a) What is your profit of the outcome if the roll is 5?

(b) Fill out the following probability distribution table. (Round your answers to two decimal places).

(c) Compute the expected value (the mean) ofX

X

. (Round your answer to the nearest hundredth.)

(d) Explain the meaning of the expected value ofX

X

in the context of this problem.

(e) If you played this game 100 times, how much would you expect to win or lose?

5) A bin contains 5 red and 4 green balls. 2 balls are chosen at random, without replacement. Let the random variable X be the number of green balls chosen.

a. Explain why X is not a binomial random variable.

b. Fill in the table to describe the probability distribution for the variable X.Round your answers to the nearest hundredth but don't round your answer until the end

6) A bin contains 3 red and 1 green balls. 3 balls are chosen at random, with replacement.

Let the random variableX

X

be the number of green balls chosen.

(a) Explain whyX

X

isa binomial random variable.

(b) Fill out the following probability distribution table. (Round your answers to four decimal places)

X

X

P(X)

(c) Find the expected value ofX

X

.

7) A test consists of 10 true/false questions. To pass the test a student must answer at least 8 questions correctly.

a. If a student guesses on each question, what is the probability that the student will answer 5 questions correctly?Round your answer to the nearest hundredth.

b. If a student guesses on each question, what is the probability that the student will pass the test?Round your answer to the nearest hundredth.

c. Find the expected number of correct answers for a student?Round your answer to the nearest hundredth.

d. Find the standard deviation of the number of correct answers.Round your answer to the nearest hundredth.

e. Is it unusual for a student to pass by guessing? Explain.

8) In a group of 40 people, 50% have never been abroad. Two people are selected at random without replacement and are asked about their past travel experience.

(a) Is this a binomial experiment?

• No
• Yes

(b) Why or why not?

(c) What is the probability that in a random sample of 2, no one has been abroad? ( answer as a fraction or round your answer to three decimal places.)

(d) What is the probability that in a random sample of 2, at least one has been abroad? answer as a fraction or round your answer to three decimal places.)