Question

Ice Cream The annual per capita consumption of ice cream (in pounds) in the United States can be approximated by a normal distribution with a mean of 15.4 lb and a standard deviation of 3.5 lb. What is the smallest annual per capita consumption of ice cream that can be in the top 25% of consumption?

Answer 1

17.76 pounds

Explanation:

The first thing we have to do is resort to the normal distribution table (attached image).

To find the smallest annual per capita consumption of ice cream that can be in the top 25% of consumption, we must find when the probability of z is equal to = 1 - 0.25 = 0.75

Find the z value when the probability 75%, i.e .:

z = invNorm (0.75) = approximately 0.675

To find the value, we apply the following formula:

x = z * sd + m

where sd is the standard deviation 3.5 and m the mean that is 15.4, knowing these values, we replace:

x = 0.675 * 3.5 + 15.4

x = 17.76

That is, the smallest annual consumption under these conditions is 17.76 pounds.