Question

The length of a pregnancy is a normal random variable with a mean of 266 days and

standard deviation of 16 days.

(a)

Find the proportion of pregnancies that are between 285 and 305 days.

(b)

A health insurance company’s family plan contained a clause stating that the

company may refuse to cover hospital costs for a birth that is less than 217

days from the date of marriage. Find the probability that a pregnancy will

last less than 217 days, and explain the logic behind the refusal of coverage

by the insurance company.

Answer 1

Solution :

Given that mean µ = 266 days and standard deviation σ = 16 days.

(a) => the proportion of pregnancies that are between 285 and 305 days is

=> P(285 < x < 305) = P((x - µ)/σ < Z < (x - µ)/σ)

= P((285 - 266)/16 < Z < (305 - 266)/16)

= P(1.1875 < Z < 2.4375)

= P(Z < 2.4375) − P(Z < 1.1875)

= 0.9927 - 0.883

= 0.1097

(b) => P(x < 217) = P((x - µ)/σ < (217 - 266)/16)

= P(Z < -3.0625)

= 1 − P(Z < 3.0625)

= 1 − 0.9989  

= 0.0011