Statistics - Required sample size for the automotive industry

(See attached file for full problem description)

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1. Use the below data to compute the sample size required for the Automotive Industry
2. Describe the independent and dependent variables
3. Include final recommendations related to defining and explaining the problem and stating the hypotheses that will be tested
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An IQ test is designed so that the mean is 100 and the standard deviation is 12 forthe population of normal adults. Find thesamplesize necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that thesample mean is within 4 IQ points of the true mean. Assume that mean = 12

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What is the mean of the sampling distribution of sample means?
What is its standard deviation?
How is that standard deviation affected by thesamplesize?
What does the central limit theorem state about that distribution?

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Test of a single proportion:
2. What is the difference between a sample parameter (X-bar and s) and a proportion parameter (p)?
Test of two populations, large samplesize (z-statistics)
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How large a samplesize is needed to detect a difference of 2.5 months from the expected value?

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2)How might one know if a samples follow a normal distribution?
Please explain each in roughly 100 words please