The annual per capita consumption of ice cream (in pounds) in the United States

Question

The annual per capita consumption of ice cream (in pounds) in the United States can be approximated by the normal distribution, as shown in the figure to the right (a) What is the largest annual per capita consumption of ice cream that can be in the bottom 20% of (b) Between what two values does the middle 80% of the consumptions lie? H18.9 #5.3 7 19 31 Consumption (in lbs) Click to view page 1 of the Standard Normal Table Click to view page 2 of the Standard Normal Table. a) The largest annual per cap ta consumption ofice cream that be in the bottom 20% of consumptions is (Round to one decimal place as needed.) pounds.

Explanation / Answer

Solution:- Given that ? = 18.9 and ? = 5.3

Also distribution is normal

a. P(X < x) = 0.10

Using z table we get P(Z<-1.282) = 0.10

So z = -1.282 = x -18.9/3.3

So x = 18.9 - 1.282*5.3 = 12.1054 = 12.1

b. P(x1 < x < x2) = 0.80

P(-1.282<z<1.282) = 0.80

So x1 =-1.282*5.3+18.9= 12.1054 = 12.1

And x2= 1.282*5.3+18.9 = 25.6946 = 25.7

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