Question

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 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. No, because random samples of 100 bags will have mean weights that vary. A mean weight around 33.6 grams is not unusual. No, because the mean weight of the sample is only off by 2 grams. Yes, because 33.6 is less than 35.6 grams

Answer 1

Answer:

As probability of that happening is very small; Yes, 33.6 is less than 35.6 grams   because   it  provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package.

Step-by-step explanation:

For a normal distribution Z-score

$Z = \frac{X-\mu}{\sigma}$

Given that :

the mean ($\mu$) = 35.6

standard deviation ($\sigma$) = 5.2

sample size (n) = 35

standard error: $\sigma_x = \frac{\sigma}{\sqrt{n}}$

$\sigma_x = \frac{5.2}{\sqrt{35}}$

$\sigma_x = 0.879$

The probability that a random sample of 35 bags has a mean weight of 33.6 grams or less is :

P(X<33.6)  = P(Z < - 2.28)

= 0.0114

Conclusion:

As probability of the happening is very small; Yes, 33.6 is less than 35.6 grams   because   it  provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package.