Chapter 8, Problem 8T

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# For the normal distribution with mean 70 and standard deviation 12, find: (a) Pr(73 ≤ x ≤ 97 ) (b) Pr(65 ≤ x ≤ 84) (c) Pr( x  > 84)

(a)

To determine

To calculate: The probability Pr(73x97) for the normal distribution where the value of mean is 70 and the value of standard deviation is 12.

Explanation

Given Information:

The value of mean is 70 and the value of standard deviation is 12

Formula used:

The z score for a normally distribution of x is,

z=xμσ

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

Calculation:

Consider the normal distribution, Pr(73x97).

The mean and standard deviation of the binomial distribution is,

μ=70 and σ=12

Since the range of interval of x is,

73x97

Use the formula to calculate z score for a normally distribution of x is,

z=xμσ

Substitute 70 for μ, 12 for σ and 73 for x.

z1=737012=0.25

Use the formula to calculate z score for a normally distribution of x is,

z=xμσ

Substitute 70 for μ, 12 for σ and 97 for x.

z2=977012=2.25

Now the conversion of x score of a normal distribution to a distribution of z score:

Pr(73x97)=Pr(0.25z2.25)

Now, the probability distribution for a z score is given as,

Pr(0

(b)

To determine

To calculate: The probability Pr(65x84) for the normal distribution where the value of mean is 70 and the value of standard deviation is 12.

(c)

To determine

To calculate: The probability Pr(x84) for the normal distribution where the value of mean is 70 and the value of standard deviation is 12.

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