   Chapter 8.4, Problem 30E ### 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 = 40 and σ = 5 . Find B so that Pr ( x > B ) =   0.12

To determine

To calculate: The value B so that Pr(x>B)=0.12 if the random variable x has normal distribution with μ=40 and σ=5.

Explanation

Given Information:

The probability is Pr(x>B)=0.12 if the random variable x has normal distribution with μ=40 and σ=5.

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=40σ=5

To find B and the condition is;

Pr(x>B)=0.12

To find this value one can use as follows:

Pr(x>B)=0.5Az0.12=0.5AzAz=0

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