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4. A tire manufacturer believes the tread life of its snow tires can be described by a normal distribution with a mean of 32,000 miles and a standard deviation of 7000 miles. Find the probability (rounding to tenth of percent) that a randomly selected tire will have a tread life:

a. of at least 40,000 miles

b. of 30,000 or less miles

c. that last between 30,000 and 35,000 miles (include the boundaries)

d. In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer doesn't want to take too big a financial risk with this guarantee. If the dealer is willing to give refunds to no more than 1 out of every 50 tires sold, for what mileage can he guarantee each tire to last ? (Round to the nearest whole number)

e. Find the probability that 50 randomly chosen tires will have a mean tread wear of greater than 35,000 miles ? (Round to tenth of a percent)

5. A final exam in Sociology has a mean of 72 and a standard deviation of 9.2. If 35 students are randomly selected, find the probability that that the mean of their test scores will be greater than 76. (Round to tenth of a percent)

6. A purchasing agent at the Kelly Bread Company wants to estimate the mean daily usage of rye flour. She takes a sample for 50 straight days and finds that the sample mean is 180 pounds with a sample standard deviation of 38.5 pounds.

a) State the 90% confidence interval for the mean.

(Round to hundredths)

b) State the margin of error (Round to tenths)

7. A high school counselor is interested in the percentage of students who will be going to college. She randomly picks 60 students and finds that 53 will be going to college. Use a 95% confidence level to find the population proportion.

a) State the 95% confidence interval for population proportion.

(Round to tenth of a percent)

b) State the margin of error (Round to tenth of a percent)

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