Question

A study reported that the length of pregnancy from conception to birth is approximately normally distributed with mean = 272 days and standard deviation σ = 9 days. Let Φ be the cdf of the standard normal distribution, express the following results in terms of Φ.

(a) (5 pts) What proportion of pregnancies last longer than 280 days?

(b) (5 pts) A pregnancy is considered full-term if it lasts between 252 days and 298 days. What proportion of pregnancies are full-term?

Answer 1

Let X be the length of pregnancy from conception to birth.

X~Normal(272 , 9)

a) P( X>280) = P( > )

= P ( z > 0.89)

= 1- P(z < 0.89)

= 1- (0.89)

b) P( 252< X < 298) = P( < < )

= P( -2. 22< z<2.89)

= P(z< 2.89) - P( z <-2.22)

= P(z< 2.89) - 1 +P(z <2.22)

= (2.89) - 1 + (2.22)