(Ross) An expert witness in a paternity suit testifies that the length (in days) of a pregnancy, from conception to delivery, is approximately normally distributed, with parameters [math]\mu = 270[/math], [math]\sigma = 10[/math]. The defendant in the suit is able to prove that he was out of the country during the period from 290 to 240 days before the birth of the child. What is the probability that the defendant was in the country when the child was conceived?

Notes

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: E

We need to calculate the probability that a normal random variable with mean 270 and standard deviation 10 lies outside the range [240,290]. This is equivalent to finding the probability that a standard normal variable [math]Z[/math] lies outside the range [-3,2]. We have [math]P(Z \lt-3) = 0.001345 [/math] and [math]P(Z \gt 2) = 0.02275[/math]. Adding these probabilities gives 0.024095.