Question

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?

Answer 1

Here, 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 15.0 gallons.

So X~ N(mean= 15.0, sd=0.15)

Now

The manufacturer of this gasoline tank consider the largest 2% of these tanks too large to put on tbe market.

Therefore we have to find tank size x such that,

P(X > x) =2% =0.02

From Z table we get

Thus the tank of size 15.3075 gallons is to be considered too large.