I am having trouble withe the following question below, specifically with e) 2. below where it seems to ask us to recalculate a new standard deviation.

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.

a) What proportion of tires wears out before 30,000 miles?

b) What proportion of tires lasts longer than 38,000 miles?

c) What proportion of tires will have a life span between 30,000 and 40,000 miles?

d) The tire manufacturer would like to advertise that 90 percent of its tires have a life span exceeding some number of miles. What's the largest such number of miles it can claim?

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.

1.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?

2. 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?