What proportion of adults use between 15 and 23 gallons of gas per week if it is normally distributed with a mean of 16 gallons and a standard deviation of 5 gallons?

Answer 1

Use z-scores. You need to find two z-scores, then find the proportion between the two using a z-table.

Formula:
z = (x - mean)/sd

For the first z:
x = 15
mean = 16
sd = 5

For the second z:
x = 23
mean = 16
sd = 5

Plug the values into the formula and calculate to find the two z-scores. Then check a z-table for the proportion between the two.