a. Domino sugar packets are labeled as containing 3.5 g. Assume that those packe

Question

a. Domino sugar packets are labeled as containing 3.5 g. Assume that those packets are actually filled with amounts that are normally distributed with a mean of 3.586 g and a standard deviation of 0.074 g. what percentage of packets have less that 3.5 g? b. Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. (Based on data from "Getting Things Fixed, " Consumer Reports). If you want to provide a warranty so that only 1% of the TV sets will be replaced before the warranty expires, what is the time length of the warranty?

Explanation / Answer

a) Mean = 3.586 g

Standard deviation = 0.074 g

P(X < 3.5) = P(Z < (3.5 - mean)/standard deviation)

= P(Z < (3.5 - 3.586)/0.074)

= P(Z < -1.16)

= 0.1230

So, 12.3% of packets have less than 3.5g

b) mean = 8.2 years

standard deviation = 1.1 years

Let A be the length of warranty

P(X < A) = 0.01

P(Z < (A - 8.2)/1.1) = 0.01

(A - 8.2)/1.1) = -2.33

A = 5.637

So, the time length of warranty should be 5.637 years

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