Chapter 8, Problem 22RE

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# Lengths of human pregnancies are normally distributed with mean 268 days and standard deviation 15 days. What percentage of pregnancies last be tween 250 days and 280 days?

To determine

To find: The percentage of human pregnancies last between 250 days and 280 days.

Explanation

Given information:

Length of human pregnancies is distributed in normal distribution.

The mean value is Î¼=268â€‰days .

The standard deviation is Ïƒ=15â€‰days .

Calculation:

Find the probability density function for normal distribution as shown below.

f(x)=1Ïƒ2Ï€eâˆ’(xâˆ’Î¼)22Ïƒ2 (1)

Here, the mean is Î¼ and the standard deviation is Ïƒ .

Substitute 268 days for Î¼ and 15 days for Ïƒ in Equation (1).

f(x)=1152Ï€eâˆ’(xâˆ’268)22Ã—152=137.599eâˆ’(x2âˆ’536x+71,824)450

Find the probability that human pregnancies last between 250 days and 280 days [P(250â‰¤Xâ‰¤280)] is shown below

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