Description of the question is in the picture provided
b) What is the probability that at least one and at most three of the male births have Klinefelter Syndrome? Give your answer to 4 decimal places.
What is the correct solution and answer?
2026-03-29 15:53:37.1774799617
Klinefelter Syndrome Statistics Probability
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You attempted to calculate $$\Pr[1 \le X < 3] = \Pr[X = 1] + \Pr[X = 2].$$ The question asks for at least one and at most three, which is the same as saying $$X \in \{1, 2, 3\}.$$ Thus you have neglected to include the case where exactly three such births occur, $\Pr[X = 3]$, in your calculation. You must calculate instead $$\Pr[1 \le X \le 3] = \Pr[X = 1] + \Pr[X = 2] + \Pr[X = 3].$$ Using the Poisson approximation to the binomial distribution as you have done, your rate parameter is $\lambda = (0.0011)(1000) = 1.1$ as you correctly calculated. Your answer should be $0.641387$.