Goodyears alphamax tires tread thickness is computed to be

Question

Question -

Goodyear's AlphaMax tire's tread thickness is computed to be normally distributed with a mean of 10 mm, and standard deviation 2 mm. There is a 50,000 miles warranty on AlphaMax. But to last that much, the tread should be7.9mm; otherwise the tire is sold as BetaHigh with a slightly lower warranty.

a. What proportion of tires are expected to be sold as BetaHigh.

b. If Goodyear wants that 30% of the tires produced should be sold as BetaHigh (say per market demand), then what should be the tread thickness threshold set as (formerly set as 7.9mm)?

What to Submit:

• Answers to (a) and (b)
• Screenshot of the code.
• .R file SEPARATELY in the section listed.