# MBS package-filling machine

6. From past experience, a package-filling machine has been found to have a process standard deviation of 0.6 ounces of product weight. A simple random sample is to be selected from the machine’s output for the purpose of determining the average weight of product being packed by the machine. For 95% confidence that the sample mean will not differ form the actual population mean by more than 0.1 ounces. What sample size is required?

E = 0.1 ounce, σ = 0.6

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For 95%, z = 1.960

Sample size required will be of 139 size.

7. Determine the limits of the 95% confidence interval for µ, given that

n = 148; = 6; and σ = 2.38.

Confidence interval:

For 95% CI , z = 1.96

95% CI =

95% CI = (n1, n2) where n1 = lower limit and n2 = upper limit

95% CI = (5.62, 6.38)

8. A mother who is interested in the true proportion of R-rated movies shown on pay TV by a cable system randomly selects 93 listings and finds 16 of them are R-rated movies. In her report to the subcommittee she wants to be 98% confident that the true proportion will be in an interval which she states. She has asked you to assist her by preparing a 98% confidence interval based on the data she collected. What should she report?

For 98% CI, z = 2.326

98% CI =

98% CI = 0.81 to 0.263

9. Determine the Limits of the 85% confidence interval for π, given that n = 60; and p = 0.15.

p = 0.15, n = 60

For 85% CI, z = 1.44

85% CI =

85%C1= 0.084 to 0.216