# Assessing Sampling distributions

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1. Find the area under the standard normal curve to the left of z = 1.93.

2. A traffic study at one point on an interstate highway shows that vehicle speeds are normally distributed with a mean of 61.3 mph and a standard deviation of 3.3 mph. If a vehicle is randomly checked, find the probability that its speed is between 55.0 mph and 60.0 mph.

3. A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

4. Suppose the annual consumption of chicken mean is 20.84 pounds per person, and that the standard deviation for the consumption of chicken per person is 9.193 pounds. The mean weight of chicken consumed for a sample of 200 randomly selected people is one value of many that form the sampling distribution of sample means.

Describe the shape of this sampling distribution.

What is the mean value for this sampling distribution?

What is the standard deviation of this sampling distribution?

5. Individual scores of a placement examination are normally distributed with a mean of 84.2 and a standard deviation of 12.8.

If the score of an individual is randomly selected, find the probability that the score will be less than 90.0.

If a random sample of size n = 20 is selected, find the probability that the sample mean will be less than 90.0.

6. A normal distributed population has a mean of 250 pounds and a standard deviation of 10 pounds. Given n = 20, what is the probability that this sample will have a mean value between 245 and 255 pounds?

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This solution answers various questions regarding sampling distributions.

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- BSc, Meerut University
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- MPhil, Institute of Advanced Studies
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