5.13 Discrete and continuous random variables: homework  (Page 2/5)

Six different colored dice are rolled. Of interest is the number of dice that show a “1.”

• d On average, how many dice would you expect to show a “1”?
• e Find the probability that all six dice show a “1.”
• f Is it more likely that 3 or that 4 dice will show a “1”? 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. (Source: http://en.wikipedia.org/wiki/Distance_education)

• d On average, how many schools would you expect to offer such courses?
• e Find the probability that at most 6 offer such courses.
• f Is it more likely that 0 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

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.

• d How many of the 12 students do we expect to attend the festivities?
• e Find the probability that at most 4 students will attend.
• f Find the probability that more than 2 students will attend.

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

• 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.

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

• d How many are expected to not use the foil as their main weapon?
• e Find the probability that six do not use the foil as their main weapon.
• f Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.

Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of high school.

• d How many seniors are expected to have participated in after-school sports all four years of high school?
• e Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.
• f Based upon numerical values, is it more likely that 4 or that 5 of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.