A study conducted by Hershey\'s discovered that Americans consumed an average of

Question

A study conducted by Hershey's discovered that Americans consumed an average of 11.4 pounds of chocolate per year. Let's assume that the annual chocolate consumption follows the normal distribution with a standard deviation of 3.6pounds a.) What is the probability that a randomly selected person (n=1) will consume i.) Less than 7 pounds of chocolate next year? ii.) More than 9 pounds of chocolate next year? iii.) Between 8 and 12 pounds of chocolate next year? iv.) Exactly 10 pounds of chocolate next year? (I believe this is zero - in theory.) b.) What is the annual consumption of chocolate that represents the 60th percentile?

Explanation / Answer

P(x-mean/sigma)

by converting them into normal distribution we should get

1>.P(Z<7-11.4/3.6)..P(Z<-1.22)=2*0.888-1= 0.776

2).P(z>9-11.4/3.6)=,,,....P(z>-0.55)= 0.6

3>.P(-0.833<z<0.167)=0.04

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