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For this question, answers should be decimal with 4 digits to right of the decimal point. ex. 0.1234 Bob owns a car rental co
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Answer #1

a) The probability that the car battery fails within 1 year is computed here as:

P(T <1) = f (1/2)e=/2 dt = 1 –e-12 0.39347

The expected number of batteries that were replaced last year is:

= np

= 10*0.39347

= 3.9347

b) Probability that Bob had to replace 4 batteries in 2019 is

Here we binomial probability function :

10 P(X = 4) = 0.393474 347*(1 – 0.39347)* = 0.2506

0.2506 is the required probability.

c) Exponential distribution follows a memoryless property, that is it does not depend on the past events. Therefore we just have to find the probability here that 2 batteries are to be replaced in 1 year

P(X = 2) = (2) 0.39347(1 – 0.39347)* = 0.1276

0.1276 is the required probability.

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