Question

Suppose the amount of heating oil used annually by households in Ontario is normally distributed with a mean of 760 liters per household per year and a standard deviation of 150 liters of heating oil per household per year.

If the members of a particular household were scared into using fuel conservation measures by newspaper accounts of the probable price of heating oil next year, and they decided they wanted to use less oil than 97.5% of all other Ontario households currently using heating oil, what is the maximum amount of oil they can use and still accomplish their conservation objective?

Answer 1

Solution:

Given: X = the amount of heating oil used annually by households in Ontario is normally distributed with a mean of 760 liters per household per year and a standard deviation of 150 liters of heating oil per household per year.

We have to find the maximum amount of oil they can use such that: they wanted to use less oil than 97.5% of all other Ontario households currently using heating oil.

That is we have to find x value such that:

P( X > x ) = 97.5%

P( X > x ) = 0.975

that is:
P( X < x) = 1 - P( X > x )

P( X < x) = 1 - 0.975

P( X < x) = 0.025

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z value = -1.96

Now use following formula to find x value:

Thus maximum amount of oil they can use and still accomplish their conservation objective is 466 liters.