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

Answer:

$P(x< 240) = 0.0521$

Step-by-step explanation:

Given

$\bar x = 266$

$\sigma = 16$

Required

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

First, calculate the z score

$z = \frac{x - \bar x}{\sigma}$

Where:

$x = 240$

So, we have:

$z = \frac{240 - 266}{16}$

$z = \frac{-26}{16}$

$z = -1.625$

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:

$P(x< 240) = 0.0521$