Question

The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of

267

days and a standard deviation of

10

days.

​(a) What is the minimum pregnancy length that can be in the top

12​%

of pregnancy​ lengths?

​(b) What is the maximum pregnancy length that can be in the bottom

5%

of pregnancy​ lengths?

*please show steps to solve for reference, thanks!

Answer 1

Given that,

mean = $\mu$ = 267

standard deviation = $\sigma$ =10

Using standard normal table,

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12

= P(Z < z ) = 1 - 0.12

= P(Z < z ) = 0.88

z = 1.18 (using standard normal (Z) table )

Using z-score formula  

x = z * $\sigma$ + $\mu$

x=1.18 *10+267

x= 278.8

b.

P(Z < z) = 5%

= P(Z < z ) =0.05

z =-1.65 (using standard normal (Z) table )

Using z-score formula  

x = z * $\sigma$ + $\mu$

x=-1.65 *10+267

x= 250.5