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blsea [12.9K]
2 years ago
9

Consider this problem: Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil an

d lube service at this garage is 15 minutes per car, and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 505 discount on the charges. The company wants to limit this discount to at most 5% of the customers. What should the maximum guaranteed waiting time be
Business
1 answer:
astraxan [27]2 years ago
6 0

Answer:

The maximum time guaranteed = 19.04 minutes.

Explanation:

From the given problem data, we have:

Let Y be the random variable which follows the normal distribution.

So,

Y ~ N(u = 15, SD = 2.4

Where, u = mean and SD = Standard Deviation

Let the maximum time guaranteed is = M

So,

P (Y > M) = 0.05   equation 1

Convert this equation 1 into standard normal variable, that is,

P(Y> M) = 0.05

1 -  P(Y \leq M) = 0.05

P(Y \leq M) = 1 - 0.05

P(Y \leq M) = 0.95

P(\frac{Y-u}{SD} \leq \frac{M-u}{SD} ) = 0.95

P ( Z \leq \frac{M - 15}{2.4} )  = 0.95     Equation 2

From the equation 2, we have,

\frac{M-15}{2.4} = 1.644853627  

1.644853627 value is from using the function of Excel

( =NORSINV(0.95)) = 1.644853627

So,

M = 1.644853627 + 2.4 + 15

M = 19.04

Hence, the maximum time guaranteed = 19.04 minutes.

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