# Answer the Questions

**Question description**

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. A sample of 35 bags is selected. So we have that the breaking strength of the bags is normal with µ=5 lbs/*in*^{2} and σ = 1.5 lbs/*in*^{2}. Also, n = 35.

1) What is the probability that the average breaking strength is between 5 and 5.5 pounds per square inch?

2) What is the probability that the average breaking strength is between 4.2 and 4.5 pounds per square inch?

3) What is the probability that the average breaking strength is less than 4.6 pounds per square inch?

4) Suppose you have selected a random sample of N-7measurements from a normal distribution. Compare the standard normal z- critical values with the corresponding *t*- critical values if you were forming the following confidence intervals:

480% confidence interval

590% confidence interval

5) The following sample of 16 measurements was selected from a population that is approximately normally distributed.

91, 80, 99, 110, 95, 106, 78, 121, 106, 100, 97, 82, 100, 83, 115, 104

6) Construct an 80% confidence interval for the population mean and interpret the interval.

7) Construct a 95% confidence interval for the population mean and interpret the interval.

8) Explain why the 80% confidence interval is narrower?

A labor union has several thousand members. In a sample of 40 union members, 32 have indicated that they are in favor of accepting the union’s current compensation plan.9) Calculate a 99% confidence interval for the population proportion of members who are in favor of the plan and interpret your results.

10) What is the sample size needed to reduce the Margin of Error to .135 at a 99% confidence level?

## Tutor Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors