Question

Essay type Questions
Chapter 8
1. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.24 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have an average weight less than 15.97 ounces?

2. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.98 inches. A sample of 49 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.93 and 30.33 inches long?

Chapter 9
3. A sample of 25 items yields X = 60 grams and s = 9 grams. Assuming a normal parent distribution, construct a 99 percent confidence interval for the population mean weight.

4. Of a random sample of 900 trucks at a bridge, 360 had bad signal lights. Construct a 99 percent confidence interval for the percentage of trucks that had bad signal lights.

5. Suppose that 80 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1600 voters would yield a sample proportion in favor of the candidate within 1 percentage points of the actual proportion.

Answer 1

Q8

1.

Given that

μ=16, σ=0.24, n=16

P(x̅<15.97) = P((x̅-μ)/(σ/√n) < (15.97-16)/(0.24/√16)) = P(z<-0.5) = 0.3085 (from z table)

the probability that 16 randomly selected packages will have an average weight less than 15.97 ounces = 0.3085

2.

μ=30.0,σ=0.98,n=49

P(29.93<x̅<30.33)=P((29.93-30.0)/(0.98/√49) < (x̅-μ)/(σ/√n) < (30.33-30..0)/(0.98/√49))

=P(-0.5<z<2.357)=P(z<2.357)-P(z<-0.5) = 0.9907-0.3085 = 0.6822

the probability that the average length of a sheet is between 29.93 and 30.33 inches long = 0.6822

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