1. A study by one automobile manufacturer indicated that 1 out of every 4 new ca

Question

1. A study by one automobile manufacturer indicated that 1 out of every 4 new cars required repairs under the company's new-car warranty, with an average cost of repair of $50.00 per repair. A. For 100 new cars, what is the expected cost of repairs? What is the variance of the expected cost? For this I found that .25 is the probability and the cost is $1250 For the variance I believe it to be .75758 But not so sure.
B. Provide a resonable estimate of the most it might cost the manufacturer for a specified group of 100 cars? (Hint: Use 3 standard deviations as your resonable limit) Completely stuck on this one.

Explanation / Answer

probability of repair is 1/4
probability of no repair is 3/4
This gives a binomial distribution.
n=100
mean =100*(1/4)=25 this is average number of cars that need repair.
since average cost is $50, $50*25=$1250 is total cost.
standard deviation of binomial distribution is (npq)={100(14)(3/4)}=4.33, since wemultipled mean by 50, we will also multiply standard deviation by 50 =$216.51 so 3standard =3*216.51=649.52.

Add that to mean 1250+649.52=1899.52 would be an estimate of most it would cost to fix 100 cars.

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