A family-owned business offers several varieties of specialty potato chips. The packaging process has been under scrutiny lately due to the complaints of several customers. Customers have primarily complained of an alleged shortage of chips in the 12 ounce bags. A random sample of 50-12oz. bags of potato chips have been removed from the assembly line and weighed to determine the validity of the customers complaints. Let X be the random variable which denotes the weight, in ounces, of each bag found below. Assume X is a normally distributed variable. After an analysis is completed, the company plans to make changes to their packaging process to ensure customer satisfaction. A second random sample of 50-12 oz bags will be taken for comparison.

Copy and paste the datasets at the bottom of the assignment into StatCrunch to answer the following questions. To find the cumulative area to the left or right of a certain value or the area between two values using StatCrunch, select the Stat button, choose Calculators and then Normal. You will need to enter the mean and standard deviation and then choose the appropriate direction for the area in which you want to calculate (< or >). You may also select Between in the upper left hand corner of the window box to calculate areas between two values. Select the Compute button to display the probability (area) and the corresponding shaded density curve. Use the software StatCrunch to answer the following questions. In this lab, you will enter the probability and select Compute to display the x-values in question.

1. Calculate the following for the original sample of 50-12 oz bags in the first column found below. The answers should be rounded to 3 decimal places.

2. Obtain the standardized version, z, of x.

3. Find the weight of bag that will separate the bottom 15% in the original sample.

4. Interpret the results in number 3 using complete sentences.

5. Find the weight of the bag that will separate the top 10% in the original sample.

6. Interpret the results in number 5 using complete sentences

7. Find the weights of bags in the original sample that will separate the middle 90% of all bags. What z-scores are associated with this range of values?

A review of the packaging process was conducted and several changes were made to improve quality control. A new sample of 50-12oz. bags have been randomly selected and weighed to determine the improvements in the packaging department.

8. Calculate the following for the second sample of 50-12 oz bags in the second column found below. The answers should be rounded to 3 decimal places.

9. Obtain the standardized version, z, of x for the second sample.

10. Find the weight of bag that will separate the bottom 15% in the second sample.

11. Interpret the results in number 10 using complete sentences.

12. Find the weight of the bag that will separate the top 10% in the second sample.

13. Interpret the results in number 12 using complete sentences.

14. Find the weights of bags in the second sample that will separate the middle 90% of all bags. What z-scores are associated with this range of values?

Weights of 50-12oz bag samples of potato chips

Original Sample in 1^st column, Sample after changes in 2^nd column

10.6 12.3

10.5 12.3

11.3 11.3

13.2 11.9

12.6 12.3

12.2 11.7

10.1 12.4

12.1 11.5

12.3 11.8

12.7 11.6

12.9 11.0

12.2 12.1

12.1 12.4

13.5 12.0

11.7 11.9

12.3 12.3

11.1 12.4

13.0 11.7

11.8 12.0

13.9 12.9

11.7 12.8

12.6 12.2

12.9 12.1

12.0 11.9

13.8 12.1

10.7 11.1

13.0 12.8

13.0 11.8

11.9 12.1

11.9 11.6

9.5 11.7

9.2 13.1

12.5 11.5

12.1 12.5

12.5 12.3

11.5 11.8

12.1 11.8

11.1 12.2

11.3 12.6

12.7 12.2

10.9 12.9

11.1 12.2

10.9 12.7

10.1 11.5

12.3 12.1

10.4 12.2

12.4 12.2

11.8 11.9

11.8 11.9

12.0 11.5