Question

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?

X is binomial with n = 20 and p = .22.

Y is binomial with n = 40 and p = .32.

Z is not binomial.

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

.105

190

7.12

.22

.05

All of the above are true.

Only (A) and (B) are true.

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.

Mean: 12.8

Standard Deviation: 2.95

Mean: 40

Standard Deviation: .32

Mean: .32

Standard Deviation: 40

Mean: 12.8

Standard Deviation: 8.704

We cannot find the mean and standard deviation since the probability distribution table is not given.

Answer 1

1).the true facts about the random variables X, Y, and Z be:-

X is binomial with n = 20 and p = .22.

Y is binomial with n = 40 and p = .32.

2). the probability that exactly 2 of the 20 older adults prefer organic be:-

3).the mean and standard deviation of the random variable Y be:-

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