A scientist believes that the gender of a child is a binomial random variable with probability = .5 for a boy and .5 for a girl. To help test her belief, she randomly samples 100 families with five children. She records the number of boys. Can the scientist infer that the number of boys in families with five children is not a binomial random variable with p = .5? (Find the probability of X = 0, 1, 2, 3, 4, and 5 from a binomial distribution with n = 5 and p = .5.)
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