# EBook Problems Normal Prob

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## Contents |

## EBook Problems Set - Nonstandard Normal Distribution: Finding Probabilities

### Problem 1

The Rockwell hardness of certain metal pins is known to have a mean of 50 and a standard deviation of 1.5. If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the average hardness for a random sample of nine pins is at least 50.5?

- Choose one answer.

*(a) Approximately 4*

*(b) 0.4*

*(c) Approximately 0.1587*

*(d) Approximately 0*

### Problem 2

In an article in the Journal of American Pediatric Health researchers claim that the weights of healthy babies born in the United States form a distribution that is nearly normal with an average weight of 7.25 pounds and standard deviation of 1.75 pounds. The US Department of Health classifies a newborn as "low birth weight" if her/his weight is less than 5.5 pounds. What is the probability that a baby, chosen at random, weighs less than 5.5 pounds?

- Choose one answer.

*(a) About 16%*

*(b) About 84%*

*(c) About 90%*

*(d) the probability cannot be determined*

*(e) About 10%*

### Problem 3

The settlement of each footing shown follows a normal distribution with a mean of 2 inches and a coefficient of variation of 30%. Suppose the settlements between two adjacent footings are correlated with a correlation coefficient of 0.7. suppose

*D* = *S*_{1} − *S*_{2}

where *S*_{1} and *S*_{2} are settlements of footings 1 and 2, respectively.

*(a) Determine the mean and variance of D.*

*(b) What is the probability that the magnitude of the differential settlement (i.e., the difference between the settlements of two adjacent footings) will be less than 0.5 inch?*

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