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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

Blood pressure Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 12. Find the probability that a woman selected at random has blood pressure (a) greater than 140. (b) less than 110.

(c) between 110 and 130.

(a)

To determine

To calculate: The probability that a woman selected at random has blood pressure greater than 140 where the mean of the normal distribution is 120 and the standard deviation is 12.

Explanation

Given Information:

Systolic blood pressure for a group of women is normally distributed and the mean is 120 and 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 blood pressure greater than 140 and the mean and the standard deviation,

μ=140 and σ=12

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

z=xμσ

Substitute 120 for μ, 12 for σ and 140 for x.

z=14012012=1.67

As normal distribution is symmetric about mean 0.5.

So this implies,

Pr(z1.67)=0

(b)

To determine

To calculate: The probability that a woman selected at random has blood pressure less than 110 where the mean of the normal distribution is 120 and the standard deviation is 12.

(c)

To determine

To calculate: The probability that a woman selected at random has blood pressure between 110 and 130 where the mean of the normal distribution is 120 and the standard deviation is 12.

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