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.

99?%

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

mu equals 18.1?=18.1

sigma equals 3.4?=3.4

Click to view page 1 of the Standard Normal Table.

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?(a) The largest annual per captita consumption of ice cream that be in the bottom

99?%

of consumptions is

nothing

pounds.

?(Round to one decimal place as? needed.)

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

99?%

of? consumptions?

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

18306Consumption (in lbs)

mu equals 18.1?=18.1

sigma equals 3.4?=3.4

xx y graph

Explanation / Answer

Solution:- Given that ?=18.1 , ?=3.4

(a) Using z table we get P(Z<2.3263)=0.99

so, z=2.3263 = x-18.1/3.4

x = 18.1 + (2.3263*3.4)

x =  26.0094

(b)

P(x1<x<x2)=0.80

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

So z1=-1.282*3.4+18.1= 13.74

Z2 = 1.282*3.4+18.1 = 22.5

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