   Chapter 8.4, Problem 29E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# The random variable x has a normal distribution with μ = − 3 and σ = 4 . Find B so that Pr ( x < B ) =   0.75

To determine

To calculate: The value B so that Pr(x<B)=0.75 if the random variable x has normal distribution with μ=3 and σ=4.

Explanation

Given Information:

The probability Pr(x<B)=0.75 if the random variable x has normal distribution with μ=3 and σ=4 is

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

Calculation:

Consider that the random variable x has normal distribution.

The mean and standard deviation is;

μ=3σ=4

Find B and the condition is,

Pr(x<B)=0.75

Find this value one can use follows,

Pr(x<B)=0

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