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People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given $Table4.37.$There is five-video limit per customer at this store, so nobody ever rents more than five DVDs.

a. Describe the random variable X in words.

b. Find the probability that a customer rents three DVDs.

c. Find the probability that a customer rents at least four DVDs.

d. Find the probability that a customer rents at most two DVDs.

A school newspaper reporter decides to randomly survey $12$students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that $18\%$of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

a. In words, define the random variable $X$.

b. List the values that $X$may take on.

c. Give the distribution of$X.X~\_\_\_\_\_(\_\_\_\_\_,\_\_\_\_\_)$

d. How many of the $12$students do we expect to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.

A school newspaper reporter decides to randomly survey $12$students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that $18\%$of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

a. In words, define the random variable $X$.

b. List the values that $X$may take on.

c. Give the distribution of $X$. $X~$_____(_____,_____)

d. How many of the $12$students do we expect to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend

Use the following information to answer the next two exercises: The probability that the San Jose Sharks will win any given game is $0.3694$based on a $13-year$win history of $382$wins out of $1,034$games played (as of a certain date). An upcoming monthly schedule contains $12$games.

The expected number of wins for that upcoming month is:

a. 1.67

b. 12

c. $\frac{382}{1043}$

d. 4.43

Let X = the number of games won in that upcoming month.

On average, how many batches should the baker make?

Use the following information to answer the next four exercises: Ellen has music practice three days a week. She practices

for all of the three days $85\%$ of the time, two days $8\%$ of the time, one day $4\%$ of the time, and no days $3\%$of the time. One

week is selected at random.

What is the probability that the San Jose Sharks win at least five games in that upcoming month

$a.0.3694b.0.5266c.0.4734d.0.2305$

A student takes a $32$-question multiple-choice exam, but did not study and randomly guesses each answer. Each question has three possible choices for the answer. Find the probability that the student guesses more than $75\%$of the questions correctly.

Six different colored dice are rolled. Of interest is the number of dice that show a one.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. On average, how many dice would you expect to show a one?

e. Find the probability that all six dice show a one.

f. Is it more likely that three or that four dice will show a one? Use numbers to justify your answer numerically.

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. On average, how many schools would you expect to offer such courses?

e. Find the probability that at most ten offer such courses.

f. Is it more likely that 12 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many are expected to attend their graduation?

e. Find the probability that 17 or 18 attend.

f. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically