, so

Now match up percentile points.

When X=35 we have the lower 7 percentile of a Z, known as -1.47 or -1.48.

That's via the tables, but you can do better via a link on line.

And when X=63 we have the upper 11 percentile of a Z, known as 1.22 or 1.23.

You now have two equations with two unknowns. Find and .

IN part (b) you have a binomial question, where n=1000 and a success is for a tire to fail before 40 months.

So .

HOWEVER, the question should ask you to APPROXIMATE this via the Central Limit Theorem.

Otherwise you need to obtain via a summation

or you can use the complement.

BUT I bet they want you to approximate via the normal distribution.

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I was just surfing and I found...

http://bayes.bgsu.edu/nsf_web/jscrip...ormal_icdf.htm

Plug in mean 0, st dev 1, prob .07 and I got....-1.4749

Plug in mean 0, st dev 1, prob .89 and I got....1.2249