Please help me do this question Question 6. An expert witness in a paternity sui

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Please help me do this question

Question 6. An expert witness in a paternity suit testifies that the length (in days) of pregnancy (that is, the time from impregnation to the delivery of the child) is approximately normally distributed with parameters 270 and 2 = 100, The defendant in the suit is able to prove that he was out of the country during a period that began 290 days before the birth of the child and ended 240 days before the birth. If the defendant was, in fact, the father of the child, what is the probability that the mother could have had the very long or very short pregnancy indicated in the testimony?

Explanation / Answer

therefore probability that pregnancy will take more than 290 days or less than 240 days =P(X<240) +P(X>290)

=1-P(240<X<290) =1-P((240-270)/10<Z<(290-270)/10)=1-P(-3<Z<2)=1-(0.9772-0.0013)=0.0241

for normal distribution z score =(X-)/ here mean=       = 270 std deviation   == 10.000

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