Six different colored dice are rolled Of interest is the num

Six different colored dice are rolled. Of interest is the number of dice that show a one. In words, define the random variable X. List the values that X may take on. Give the distribution of X.X~ On average, how many dice would you expect to show a one? Find the probability that all six dice show a one. 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. In words, define the random variable X. List the values that X may take on. Give the distribution of X X~ On average, how many schools would you expect to offer such courses? 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. In words, define the random variable X. List the Values that X may take on. Give the distribution of X. X ~ How many are expected to attend their graduation? Find the probability that 17 or 18 attend. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.

Solution

96.

a.

the random variable x is the number of students attend their graduation

b.

X may take tha value s in between 0,1,2,3,,,,,22

c.

X Follows Binomial with ( 22, 0.85)

d.

expected = 22*0.85 = 18.7

e.

P( X = 17 ) = ( 22 17 ) * ( 0.85^17) * ( 1 - 0.85 )^5
= 0.1262
P( X = 18 ) = ( 22 18 ) * ( 0.85^18) * ( 1 - 0.85 )^4
= 0.1987
P( X = 17 or 18) = 0.1262+0.1987 = 0.3249