1. A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 175 and a standard deviation of 15. If an applicant is randomly selected, find the probability of a rating that is between 150 and 200.

2. A final exam in Math 157 is normally distributed and has a mean of 75 with a standard deviation of 12. If 36 students are randomly selected, find the probability that the mean of their test scores is greater than 70.

3. The weights of certain machine components are normally distributed with a mean of 9.75g and a standard deviation of 0.08g. Find the weights that separate the top 5% and the bottom 5%.

4. Use the margin of error E = $10, confidence level of 99%, and σ = $40 to find the minimum sample size needed to

estimate an unknown population mean, .μ

5. Build a 95% confidence interval for the mean of the population from the given sample data. Assume that the population has a normal distribution.

16.4, 15.7, 16.2, 15.8 17.1

15.8, 15.9, 16.0, 16.4 15.0

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