Let the random variable x represent the number of girls in a family with three c
ID: 3150127 • Letter: L
Question
Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.31. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? Find the mean of the random variable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. mu = (Round to two decimal places as needed.) The table is not a probability distribution. Find the standard deviation of the random variable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to two decimal places as needed.) The table is not a probability distribution. Is it unusual for a family with three children to have only girls? Yes, because the probability of having 3 girls is greater than 0.05. No, because the probability of having 3 girls is greater than 0.05.Explanation / Answer
A) For probbaility distribution table, Mean, E(X)=summation xi*P(xi)=0*0.329+1*0.443+2*0.199+3*0.029=0.928~0.93
A) Standard deviation: sqrt[summation (xi-xbar)^2*P(xi)]
sqrt [(0-0.93)^0.329+(1-0.93)^2*0.443+(2-0.93)^2*0.199+(3-0.93)^2*0.029]=0.799~0.80
B) The probbaility of having 3 girls is greater than 0.05.
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