statistics-determining t-critical value-z-critical value-constracting confidence interval,confidence

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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

and σ = 1.5 lbs/in

. 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?

Solution

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

and σ = 1.5 lbs/in

. Also, n = 35.

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

square inch?

( )

5.5 5

1.972

/ 1.5 / 35

5 5.5

0 1.972

0.975 0.5

0.475

P X

P z

− −

= = =

< <

= < <

= −

The probability is 0.475.

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

square inch?

4.2 5

3.155

/ 1.5 / 35

LOWER

− −

= = = −

4.5 5

1.972

/ 1.5 / 35

UPPER

− −

= = = −

Hence, the probability is:

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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 ?=5 lbs/in2?and ? = 1.5 lbs/in2. 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 ind ...
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