The lengths of pregnancies are normally distributed with a mean of 268 days last

Question

The lengths of pregnancies are normally distributed with a mean of 268 days lasting 308 days or longer b. If the length of pregnancy is in the lowest 2%, then the baby is premature. Find the length that separates premature babies from those who are not premature. a. The probability that a pregnancy will last 308 days or longer is b. Babies who are born on or before days are considered premature. Assume that women's heights are normally distributed with a mean given by mu = 63.1 in, and a standard deviation given by sigma = 2.7 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 64 in. (b) If 35 women are randomly selected, find the probability that they have a mean height less than 64 in. (a) The probability is approximately (b) The probability is approximately

Explanation / Answer

1) mean = 268 , s = 15

a)P(X > 308)

Z = (X - 268)/15

hence

P(X> 308)

=P(Z>(308 - 268)/15)

=P(Z> 40/15)

=P(Z> 2.6666)

=0.0038

b) P(Z < z*) = .02

z* = -2.054

hence

X* = 268 -2.054*15

=237.19

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