# Calculation of probabilities associated with normal distributions

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a) Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the percentage of trees having a diameter greater than 15 inches.

b) White blood cell (WBC) count per cubic millimeter of whole blood follows approximately a Normal distribution with mean 7500 and standard deviation 1750. What percentage of people have WBC between 7000 and 8000?

c) Lifetimes of a certain brand of tires is approximately normally distributed with mean 42,500 miles and standard deviation 3,200 miles. What percentage of tires will last more than 50,000 miles?

d) The incomes of a set of factory workers happen to be normally distributed.  The average income is \$53,000 and the standard deviation is \$9,000.

1.   What is the probability that a randomly selected employee makes more than \$65,000?
2. What is the probability that the average of 4 randomly selected employees makes more than \$65,000?
3. What is the probability that the average of 12 randomly selected employees makes more than \$65,000? 