# EBook Problems Normal Prob

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## 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

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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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