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.

(a) What is the largest annual per capita consumption of ice cream that can be in the bottom 10% of consumptions?

(b) Between what two values does the middle 80% of the consumptions lie?

=16.8

=4.3

(a) The largest annual per captita consumption of ice cream that be in the bottom 10% of consumptions is _____ pounds.

(Round to one decimal place as needed.)

(b) The middle 80% of consumption lies between _____ and _____ pounds.

(Round to one decimal place as needed.)

=16.8

=4.3

Explanation / Answer

Here it is given that mean=16.8 and sd=4.3

Also distribution is normal

a. We need to find x, such that P(X<x)=0.10

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

So z=-1.282=x-16.8/4.3

So x=11.2874

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

Again we have P(-1.282<z<1.282)=0.80

So z1=-1.282*4.3+16.8=11.2874

And z2=22.3126

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