A certain model of automobile tire wears out after a normally distributed number of miles, with a mean of 33,000 miles and a standard deviation of 5,000 miles.

e. The tire manufacturer would like to advertise that 95 percent of its tires have a life span exceeding 30,000 miles. Currently, 95% of the tires have a life span that exceeds 24,775 miles.

i)Assume that by using superior materials, the manufacturer can improve the mean life span, but not change the standard deviation. For what mean life span will 95% of the tires have a life span exceeding 30,000 miles?

ii)Assume that by using improved manufacturing practices, the manufacturer can reduce the standard deviation of the life span, not changing the mean. For what standard deviation will 95% of the tires have a life span exceeding 30,000 miles?