The Normal Distribution-

For all problems be sure to use the following 3 steps:

(i) Sketch a bell curve and shade the area corresponding to the probability you want

(ii) Find the appropriate z-score(s)

(iii) Determine the appropriate probability

1. The number of gallons of Gatorade consumed by a football team during a game follows a normal distribution with mean 20. The standard deviation is 3.  If a game is selected at random, find the probability that the number of gallons consumed will be:

(a)  Greater than 18 gallons.

(b)  Between 22 and 25 gallons.

(c) Less than 16 gallons.

2. The average diastolic blood pressure of a certain age group of people is 85 mmHg, and follows a normal distribution. The standard deviation is 6.  If an individual is selected at random, find the probability that the individual's pressure will be:

(a) Greater than 90

(b) Between 90 and 95.

(c) Between 82 and 90.

3. An automobile dealer finds that the average price of a used car is $9,000.  He decides to sell cars that appeal to the middle 70% of the market in terms of price. Find the minimum and maximum prices of the cars the dealer will sell. The standard deviation is $1,300 and the distribution of prices is normal.

4. The average weight of a group of young adults is 160 pounds. The standard deviation is 10. If a sample of 49 is taken from this group, find the probability that the sample mean for the 49 will be less than 155 pounds.