Question

# The total amount of time it takes a JC Auto Repair mechanic to complete a full-service,...

The total amount of time it takes a JC Auto Repair mechanic to complete a full-service, 16-point oil change is distributed as a uniform random variable, ranging from 18 to 32 minutes.

What is the standard deviation of service time? Report your answer to 2 decimal places using conventional rounding rules.

What is the probability that the amount of time to complete a full service, 16-point oil change will be less than 28 minutes? Report your answer to 4 decimal places using conventional rounding rules.

What is the probability that the amount of time to complete a full service, 16-point oil change will be between 19 and 23 minutes? Report your answer to 4 decimal places using conventional rounding rules.

What is the average amount of time to complete a full service, 16-point oil change at Grease Monkey? Report your answer to 2 decimal places using conventional rounding rules.

Solution :

Given that,

a = 18

b = 32

a) standard deviation =  (b - a) / 12

standard deviation =  (32 - 18) / 12

standard deviation = 4.04 minutes

b) P(x < c) = (c - a) / (b - a)

P(x < 28) = (28 - 18) / (32 - 18)

P(x < 28) = 0.7143

c) P(c < x < d) = (d - c) / (b - a)

P(19 < x < 23) = (23 - 19) / (32 - 18)

P(19 < x < 23) = 0.2857

d) Average = (a + b) / 2

Average = (18 + 32) / 2

Average = 25

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