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A food manufacturing company has taken a sample of its packaged products. For the 700 packages...

A food manufacturing company has taken a sample of its packaged products. For the 700 packages sampled and weighed, the mean weight is 6.42 oz with a standard deviation of 0.7 oz. Find the probability that a random sample of 100 packages chosen from this group will have a combined weight of more than 690 oz.

Math   Statistics-And-Probability   
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Answer #1

Here we have

Since

So it is necessary to apply the finite population correction factor.

Here finite population correction factor is

The standard error will be

The sample total 690 oz means sample mean 690 /100 = 6.9 oz

The sampling distribution of sample mean will be approximately normal with mean

The z-score for is

The probability that a random sample of 100 packages chosen from this group will have a combined weight of more than 690 oz is

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