Let the random variable x represent the number of girls in a family with three c
ID: 3174144 • 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 0.49. 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?
x P(x)
0 0.133
1 0.382
2 0.367
3 0.118
Find the mean of the random variable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. = __ (Round to two decimal places as needed.)
B. 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.
A. =__ (Round to two decimal places as needed.)
B. The table is not a probability distribution.
Is it unusual for a family with three children to have only girls?
A. Yes, because the probability of having 3 girls is greater than 0.05.
B. No, because the probability of having 3 girls is greater than 0.05.
C. No, because the probability of having 3 girls is less than or equal to 0.05.
D. Yes, because the probability of having 3 girls is less than or equal to 0.05.
Explanation / Answer
a) mean, E(X) = 0 * 0.133 + 1 * 0.382 + 2 * 0.367 + 3 * 0.118
= 1.47
b) E(X2) = 02 * 0.133 + 12 * 0.382 + 22 * 0.367 + 32 * 0.118
= 2.912
Var(X) = E(X2) - (E(X))2
= 2.912 - 1.472
= 0.7511
Standard deviation = sqrt(0.7511) = 0.87
c) Option-B. No, because the probability of having 3 girls is greater than 0.05.
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