Question

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.*

ANSWER:

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.*

ANSWER:

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.*

ANSWER:

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.*

ANSWER:

Answer #1

a)

Here, the given values of lower limit, a = 18 and upper limit, b =
32

For Uniform distribution,

Standard Deviation = sqrt((b - a)^2/12)

Standard Deviation = sqrt((32 - 18)^2/12 = 4.04

b)

For Uniform Distribution,

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

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

P(X <= 28) = 0.7143

c)

For Uniform Distribution,

P(x1 <= X <= x2) = (x2 - x1)/(b - a)

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

P(19 <= X <= 23) = 0.2857

d)

Mean = (a + b)/2

Mean = (18 + 32)/2 = 25

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.
ANSWER:
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...

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