   Chapter 8, Problem 29RE ### 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

# If a variable x is normally distributed, with μ  = 25 and σ  = 5, find Pr ( 20  ≤   x   ≤  30 ) .

To determine

To calculate: The value of Pr(20x30) if a variable x is normally distributed, with μ=25 and σ=5.

Explanation

Formula used:

For a binomial distribution:

Mean is μ=np and standard deviation is σ=npq

And z score is, z=xμσ

q=1p

Where n the number of trials, p is the probability of success, and q is the probability of failure.

Calculation:

Consider a variable x is normally distributed, with μ=25 and σ=5. Then the value of Pr(20x30).

To find the Pr(20x30) we convert 25 and 30 into z scores using z=xμσ.

Computing the z scores,

z=xμσz20=20255z20=55z20=1

And,

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