Assuming that the price of gas per gallon in a city is normally distributed with

Question

Assuming that the price of gas per gallon in a city is normally distributed with a mean of $1.90 and a standard deviation of $0.10, answer the following questions:

a. What percent of gas stations charge within ± 10¢, 20¢, and 30¢ around the mean?

b. Find two prices symmetrically around the mean in which 90% of gas stations charge within those two prices..

c. Find two prices symmetrically around the mean in which 95% of gas stations charge within those two prices.

d. Find two prices symmetrically around the mean in which 99% of gas stations charge within those two prices.

e. What is the probability a gas station selected at random charge more than $2.50.

Explanation / Answer

c.using Empirical rule of the normal distribution the two values prices symmetrically around the mean in which 95% of gas stations charge within those two prices is +2 and -2.

That is 1.90+2*0.10=2.1 and 1.90-2*0.10=1.7

d. using Empirical rule of the normal distribution the two values prices symmetrically around the mean in which 99% of gas stations charge within those two prices is +3 and -3.

That is 1.90+3*0.10=2.2 and 1.90-3*0.10=1.6

e.For X=2.50, z=(x-)/=(2.50-1.90)/0.10=6

P(X>2.5)=P(z>6)=1-0=1

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