A restaurant chain wants to create dishes that will attract new clientele. They are interested in adding some organic options to their menu. A survey revealed that 22% of people over 50 and 32% of people under 50 prefer organic foods. The restaurant wants to poll their clientele.
60 clients were randomly selected: 20 older adults and 40 younger adults.
Let X be the number of older adults (out of 20) who prefer organic.
Let Y be the number of younger adults (out of 40) who prefer organic.
Let Z be the total number in the sample who prefer organic (out of 60).
1) Which of the following is true about the random variables X, Y, and Z?

a) X is binomial with n = 20 and p = .22.
b) Y is binomial with n = 40 and p = .32.
c) Z is not binomial.
d) All of the above are true.

2) What is the probability that exactly 2 of the 20 older adults prefer organic? (Note: Some answers are rounded.)

a) .105 b) .190 c) .12 d) .22 e) .05

3) What is the mean and standard deviation of the random variable Y (the number of younger adults out of 40 who prefer organic)? Answers may be rounded.

a) Mean: 12.8
Standard Deviation: 2.95
b) Mean: 40
Standard Deviation: .32
c) Mean: .32
Standard Deviation: 40
d) Mean: 12.8
Standard Deviation: 8.704
e) We cannot find the mean and standard deviation since the probability distribution table is not given.