Question

Dr. smith determined that that the average human pregnancy is 266 days from conception to birth. Assume the length of human pregnancies can be approximated by a normal distribution with a mean of 266 days and standard deviation = 16 days. Find the prob. that a pregnancy will last:__________

Answer 1

`P(x< 240) = 0.0521`

Explanation:

Given

`\bar x = 266`

`\sigma = 16`

Required

`P(x < 240)` --- pregnancy will last less than 240 days

First, calculate the z score

`z = (x - \bar x)/(\sigma)`

Where:

`x = 240`

So, we have:

`z = (240 - 266)/(16)`

`z = (-26)/(16)`

`z = -1.625`

So:

`P(x< 240) = P(z < -1.625)`

From z probability:

`P(z < -1.625) = 0.052081`

`P(z < -1.625) = 0.0521` --- approximated

So:

`P(x< 240) = 0.0521`