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

Question

05-05-2020
Mathematics

contestada

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

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-05-11T08:15:18+02:00

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

[tex]Z = \frac{X-\mu}{\sigma}[/tex]

Given that :

the mean ([tex]\mu[/tex]) = 35.6

standard deviation ([tex]\sigma[/tex]) = 5.2

sample size (n) = 35

standard error: [tex]\sigma_x = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_x = \frac{5.2}{\sqrt{35}}[/tex]

[tex]\sigma_x = 0.879[/tex]

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.