The Problem

The average number of gallons of lemonade consumed by the football team during a game is 20, with a standard deviation of 3 gallons. Assume that the variable is normally distributed. When a game is played, find the probability of using

a) Between 20 and 25 gallons
b). Less than 19 gallons
c). More than 21 gallons
d). Between 26 and 28 gallons

a) Between 20 and 25 gallons

From the text of the problem we know that = 20 and that = 3. The TI83/84 calculator provides a program to compute the probabilities of normal distributions. We use the function:

Since we need the area under the normal curve between 20 and 25, or 20 < x < 25, we let = 20 and = 25.

From the calculator home screen, press 2nd VARS[DISTR], press 2 to select 2:normalcdf(. Enter 20,25,20,3) and then press ENTER. See the results below.

 

Thus the P(20 < X < 25) = 0.4522



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