Question

A particular college has a 30% graduation rate. If 212 students are randomly selected, answer the following.

a) Which is the correct wording for the random variable? Select an answer

b) Pick the correct symbol: ? = 212 c) Pick the correct symbol: ? = 0.3

d) What is the probability that exactly 65 of them graduate with a degree? Round final answer to 4 decimal places.

e) What is the probability that less than 65 of them graduate with a degree? Round final answer to 4 decimal places.

f) What is the probability that more than 65 of them graduate with a degree? Round final answer to 4 decimal places.

g) What is the probability that exactly 66 of them graduate with a degree? Round final answer to 4 decimal places.

h) What is the probability that at least 66 of them graduate with a degree? Round final answer to 4 decimal places.

i) What is the probability that at most 66 of them graduate with a degree Round final answer to 4 decimal places

Answer 1

a) Random variable : The number of students graduate with a degree.

b) n= 212 ( number of trials / number of students selected)

c)p =0.3 ( probability of success)

d) Let X be the number of students graduate with a degree

X follow Binomial with n = 212 , p =0.3

Probability mass function of X  is

, x= 0,1,2,....212

To find P( X=65)

e) To find P( X < 65)

f) To find P( X < 65)

= 1- 0.6156

= 0.3844

g) To find P( X=66)

h) To find

=0.3844

i)To find

=0.6710

Note : Using excel formula

P( X < 65) = "=BINOM.DIST(64,212,0.3,cumulative)"

= " =BINOM.DIST(66,212,0.3,cumulative)"

P( X=65) = "=BINOM.DIST(65,212,0.3,probability mass function)"