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.The manufacturer of this gasoline tank considers the largest 2% of these tanks too large to put on the market.How large does a tank have to be to be considered too large?
A)15 gallons
B)15.31 gallons
C)15.72 gallons
D)16 gallons

Question

Quizplus · Accepted Answer

To find the cutoff for the largest 2% of tanks, we look for the z-score corresponding to the top 2% in a standard normal distribution, which is approximately 2.05. Using the formula for converting a z-score to an actual value: X = μ + zσ, where μ is the mean (15.0 gallons), σ is the standard deviation (0.15 gallons), and z is the z-score (2.05). Plugging in these values gives X = 15.0 + (2.05)(0.15) = 15.3075, which rounds to 15.31 gallons.

A Gasoline Tank for a Certain Car Is Designed to Hold