Question: Suppose Goodyear Tires manfacture tires having the property that the mileage the tire lasts follows a normal distribution with mean 70,000 and standard deviation 6400 miles.

a. What proportion of times will last at least 75, 000 miles?

b. Suppose Goodyear warrants the tires fo 60,000 miles. What proportion of ties will last 60,000 miles or less?

c. Suppose Goodyear wants to warrant no more that 2% of its ties. What mileage should the company advertise as its warranty mileage?

d. Suppose a quality control engineer obtains a simple random sample of n=10 times and calculates the mean mileage for the 10 ties. Describe the distribution athat x, the sample mean belongs to. (Hint: shape, center and spread)

e. What is the probability that a f\random samples of 10 tirre will result in a sample mean of at least 72,500 miles?

f, Suppose that a quality engineer obtains a simple random sample of n=50 tires and calculates the mean mileage for the 50 tires. What is the distribution that x belongs to? What effect does increasing the sample size have on ?

g. What is the probability that a random sample of 50 tires will result in a sample mean of at least 72,500 miles?

h Suppose that instead of the mileage that the tire lasts is heavily skewer to the lest. Would you sill be able to answer the questions in part a, b, d, and e? Why or why not?

i. Suppose that instead of the mileage that the tire lasts is heavily skewed to the left. Would you still be able to answer the question in parts f and g? Why or why not?