The lengths of pregnancies are normally distributed with a m

The lengths of pregnancies are normally distributed with a mean of 269 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 308 days or longer. b. If the length of pregnancy is in the lowest 3%, 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 _____________

(Round to four decimal places as needed.)

b. Babies who are born on or before ____________ days are considered premature.

(Round to the nearest integer as needed.)

Solution

x= length of pregnancy..

a)p( pregnancy lasting 308 days or longer) = p( x>=308) = p ( z >= ( 308 -269 ) / 15 ) = 1 - p ( z < 2.6 )
= 1- 0.9953388 =  0.0047......

b) z= (x-mean) / s.d = ( x - 269) / 15
Now, z for a bottom 3% of the popuklation = -1.880794

so, x = ( -1.880794 * 15 ) + 269 = 240.78809 which is nearly equal to 241......

so, when the length of pregnency is less than or equal to 241, the baby is premature!