Question

Bags of a certain brand of potato chips say that the net weight of the contents is 35.6 grams. Assume that the standard deviation of the individual bag weights is 5.2 grams.

A quality control engineer selects a random sample of 100 bags. The mean weight of these 100 bags turns out to be 33.6 grams.

Use this information to answer the questions below.

1. We can use a normal probability model to represent the distribution of sample means for which of the following reasons? Check all that apply.

Group of answer choices

a) the sample is randomly selected

b) the distribution of the variable in the population is normally distributed

c) the sample size is large enough to ensure that sample means will be normally distributed.

2. What is the standard error for the distribution of sample means? Group of answer choices : [5.2, 0.52, 0.13]      

What is the Z-score for the observed sample? Group of answer choices: [0.38, –0.38, 3.85, –3.85]      

What is the probability that a random sample of 100 bags has a mean weight of less than 33.6 grams? Group of answer choices: (0.3520, 0.0001)

3. Does the sample provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package?

Group of answer choices

a)Yes, because a random sample of 100 bags with a mean weight below 33.6 grams is very unlikely if the individual bags have a mean weight of 35.6 grams.

b) No, because random samples of 100 bags will have mean weights that vary. A mean weight of around 33.6 grams is not unusual.

c) No, because the mean weight of the sample is only off by 2 grams.

d) Yes, because 33.6 is less than 35.6 grams.

Answer 1

(1) The correct answer choices:

a) the sample is randomly selected.

c) the sample size is large enough to ensure that sample means will be normally distributed.

(2) The standard error for the distribution of sample means is 0.52

>> The Z-score for the observed sample is –3.85
>> The probability that a random sample of 100 bags has a mean weight of less than 33.6 grams is 0.0001

(3) a) Yes, because a random sample of 100 bags with a mean weight below 33.6 grams is very unlikely if the individual bags have a mean weight of 35.6 grams.

CALCULATIONS: