A survey asked high school seniors how many children they would like to have aft

Question

A survey asked high school seniors how many children they would like to have after they get married. A probability distribution was created to display the probability of XX, children. It is X 0 1 2 3 4 5 6 7 P(X) 0.237 0.193 0.309 0.185 0.05 0.014 0.01 0.002 This distribution has a mean of 1.71 children and a standard deviation of 1.33 children. Find the following probabilities. A. What proportion of this probability distribution is within one standard deviation of the mean? . Proportion = B. What proportion of this probability distribution is within two standard deviations of the mean? Proportion =

Explanation / Answer

a) mean + sd = 1.71 + 1.33 = (0.38 , 3.04)

P(distribution is within one standard deviation of the mean) = P(0.38 < X < 3.04)

                                                                                       = P(X = 1) + P(X = 2) + P(X = 3)

                                                                                       = 0.193 + 0.309 + 0.185

                                                                                       = 0.687

b) mean + 2*sd = 1.71 + 2*1.33 = (-0.95 , 4.37)

P(distribution is within two standard deviation of the mean) = P(-0.95 < X < 4.37)

                                                                                       = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 5)

                                                                                       = 0.237 + 0.193 + 0.309 + 0.185 + 0.05

                                                                                       = 0.974

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