Question

At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 25 minutes and the standard deviation 3

minutes.

1. What is the probability that a randomly selected car's inspection time

is between 20 and 31 minutes? Round your answer to three decimal places.

2. The owner of this auto parts places will give a gift card to the customer if his

car takes more than the longest 5% of the inspection time. What is the required

inspection time to get a gift card? Round your answer to three decimal places.

3. This place also offers a free car wash and the relationship between the car's

inspection time and washing time can be written as

            inspection time = 1.5 x washing time + 2.5

What are the mean and variance of total {inspection and washing} time?

Answer 1

Answer:-

Given that:-

At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 25 minutes and the standard deviation 3

minutes.

1. What is the probability that a randomly selected car's inspection time

is between 20 and 31 minutes?

We need to compute . The corresponding z- values needed to be computed are:

Therefore, we get

2. The owner of this auto parts places will give a gift card to the customer if his

car takes more than the longest 5% of the inspection time. What is the required

inspection time to get a gift card?

The value of that solves the equation above cannot be made directly,it is solved either by looking at a standard normal distribution table or by approximation (the way Excel or this calculator does)

Based on this, we find that the solution is ,because from the normal table we see that

Therefore,the percentile we are looking for is computed using the following formula

  

3. This place also offers a free car wash and the relationship between the car's

inspection time and washing time can be written as

            inspection time = 1.5 x washing time + 2.5

What are the mean and variance of total {inspection and washing} time?

i=1.5*w+2.5

mean=E(i)=E(1.5*w2.5)=1.5*E(w)+2.5=1.5*25+2.5=40

Variance=V(i)=V(1.5*w+2.5)= *Var(w)+0=

Since Var(constant)=0