The average number of pounds of candy that an American consu

The average number of pounds of candy that an American consumes per year is 25 pounds. Assume that the standard deviation is 2.1 pounds and the distribution is approximately normal.

a. Find the probability that a person selected at random consumes less than 23.6 pounds per year.

b. If a sample of 20 individuals is selected, find the probability that the mean of the sample will be less than 26.2 pounds per year.

c. If a sample of 20 individuals is selected, find the probability that the mean of the sample will be between 24.5 and 26.2 pounds per year.

Solution

a. Find the probability that a person selected at random consumes less than 23.6 pounds per year.

P(X<23.6) = P((X-mean)/s <(23.6-25)/2.1)

=P(Z<-0.67) = 0.2514 (from standard normal table)
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b. If a sample of 20 individuals is selected, find the probability that the mean of the sample will be less than 26.2 pounds per year.

P(xbar<26.2) = P((xbar-mean)/(s/vn)<(26.2-25)/(2.1/sqrt(20)))

=P(Z<2.56) =0.9948 (from standard normal table)

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c. If a sample of 20 individuals is selected, find the probability that the mean of the sample will be between 24.5 and 26.2 pounds per year.

P(24.5<xbar<26.2) = P((24.5-25)/(2.1/sqrt(20)) <Z< (26.2-25)/(2.1/sqrt(20)))

=P(-1.06<Z<2.56) = 0.8502 (from standard normal table)