Let p=0.2 be the proportion of smart phone owners who have a given app. For a particular smart phone owner, let x=1 if they have the app and x=0 otherwise. For a random sample of 50owners, complete parts a through e below.

a. State the population distribution (that is, the probability distribution of X for each observation).

P(X=1)= ____ and P(X=0)= _____

(Type integers or decimals. Do not round.)

b. State the data distribution if 30 of the 50 owners sampled have the app. (That is, give the sample proportions of observed 0s and 1s in the sample.)

The proportion for x=1 is __ and the proportion for x=0 is ____.

(Type integers or decimals. Do not round.)

c. Find the mean of the sampling distribution of the sample proportion who have the app among the 50 people.

mean= ____ (Type an integer or a decimal. Do not round.)

d. Find the standard deviation of the sampling distribution of the sample proportion who have the app among the 50 people. standard deviation= ___(Round to three decimal places as needed.)

e. Explain what the standard deviation in part d describes.

Which sentence below best describes the standard deviation?

A. The variability in the proportion for this sample.

B. The variability in the sample proportion across all possible samples of size50.

C. The variability in the sample proportion across all possible samples.

D. The variability in the proportion for a population of size 50.

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