A gasoline tank for a certain car is designed to hold 15 gallons of gas.Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons.What proportion of tanks will hold between 14.75 and 15.10 gallons of gas?
A)0.35
B)0.6563
C)0.6997
D)0.9833

Question

Quizplus · Accepted Answer

To find the proportion of tanks that hold between 14.75 and 15.10 gallons, calculate the z-scores for both values and use the standard normal distribution table. The z-score for 14.75 is (14.75-15.0)/0.15 = -1.67, and for 15.10 is (15.10-15.0)/0.15 = 0.67. The proportion between these z-scores is approximately 0.6997.

A Gasoline Tank for a Certain Car Is Designed to Hold