A census collected data on everyone that lived in a certain small town. The rand

Question

A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls out of four children born to a randomly selected couple in that town. Its probability distribution is shown below. Complete parts a through c. a. Find and interpret the mean of the random variable. mu_x = (Round to four decimal places as needed.) Interpret the mean. Choose the correct answer below. A. As the number of observations, n, decreases, the mean of the observations will approach the mean of the random variable. B. The observed value of the random variable will be less than the mean of the random variable in most observations. C. As the number of observations, n, increases, the mean of the observations will approach the mean of the random variable. D. The observed value of the random variable will be equal to the mean of the random variable in most observations. b. Obtain the standard deviation of the random variable. sigma_x = (Round to four decimal places as needed.) c. Draw a probability histogram for the random variable. Choose the correct graph below.

Explanation / Answer

a) mean =1.8362

option C is correct as number of observations n increases.......

b)

std deviation =(4.5598-1.83622)1/2 =1.0900

option D is correct

x P(x) xP(X) 0 0.1452 0 1 0.2014 0.2014 2 0.3778 0.7556 3 0.2232 0.6696 4 0.0524 0.2096 1.8362

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