Chapter 2.2, Problem 44E

(a)

To determine

To find: the percent of bags that weigh less than 9.02 ounces

Answer to Problem 44E

Approximately 2.5% of bags weigh less than 9.02 ounces.

Explanation of Solution

Calculation:

The distribution of weights is approximately N (9.12, 0.05). Figure below is a sketch of the Normal density curve with the desired points labeled.

  

By the 68-95-99.7 rule, approximately 2.5% of bags weigh less than 9.02 ounces, because 9.02 is two standard deviations below the mean.

  

Conclusion:

Hence,approximately 2.5% of bags weigh less than 9.02 ounces

(b)

To determine

To find: the weight range where the middle 68% of bags fall

Answer to Problem 44E

Approximately 68% of bags have weights between9.07 ounces and 9.17 ounces.

Explanation of Solution

Calculation:

By the 68-95-99 7 rules, approximately 68% of bags have weights between $9.12-0.05=9.07$ ounces and $9.12+0.05=9.17$ ounces.

  

Conclusion:

Therefore, approximately 68% of bags have weights between 9.07 ounces and 9.17 ounces.

(c)

To determine

To find: the percent of 9-ounce bags weigh between 8.97 and 9.17 ounces

Answer to Problem 44E

Approximately 83.85% of bags have weight between 8.97 and 9.17 ounces.

Explanation of Solution

Calculation:

By the 68-95-99.7 rule, that is approximately $84\%\left(0.68+0.16\right)$ of bags have weights lessthan 9.17 ounces, because 9.17 is one standard deviation above the mean. Approximately 0.15% of bags have weight less than 8.97 ounces, because 8.97 is three standard deviations below the mean. So approximately $84\%-0.15\%=83.85\%$ of bags have weight between 8.97 and 9.17 ounces.

  

Conclusion:

Therefore,83.85% of bags have weight between 8.97 and 9.17 ounces.

(d)

To determine

To find: the percentile of distribution which weighs 9.07 ounces

Answer to Problem 44E

9.07 is the 16^th percentile of the weights of these potatochips bags.

Explanation of Solution

Calculation:

The value 9.07 is one standard deviation below the mean. This means that the area to theleft of 9.07 is 0.16. In other words, 9.07 is the 16^th percentile of the weights of these potato chips bags.

Conclusion:

Therefore, 9.07 is the 16^th percentile of the weights of these potatochips bags.