Question

Over the past month, a garment manufacturer produced 800 dresses. The distribution of the amount of fabric required to make the dresses is

not normal.

The average amount of fabric needed to make a dress is 4 yards, with a standard deviation of 2 of a yard. Suppose a series of samples, each

containing 180 dresses, are selected from the dresses produced in the past month.

Would it be appropriate to model the distribution of a sample mean with a normal model?

Answer 1

yes

Explanation:

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Answer 2

Yes it will be appropriate to model the distribution of a sample mean with a normal model

Explanation:

Given that the population is not normal, and the sample is sufficiently large, according to the Central Limit theorem, the distribution of the mean pf the sampling distribution will be approximately normal not withstanding the population from which the sample is obtained. Therefore, the mean,
`\overline x`, and the standard deviation,
`(\sigma)/(√(n) )`, of the sample will be equal to the mean, μ, and standard deviation, σ, of the of the population

Therefore, it will be appropriate to model the distribution of a sample mean with a normal model