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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

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 μ=268days .

The standard deviation is σ=15days .

Calculation:

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

f(x)=1σ2πe(xμ)22σ2 (1)

Here, the mean is μ and the standard deviation is σ .

Substitute 268 days for μ and 15 days for σ in Equation (1).

f(x)=1152πe(x268)22×152=137.599e(x2536x+71,824)450

Find the probability that human pregnancies last between 250 days and 280 days [P(250X280)] is shown below

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