A restaurant believes that two of the most important factors that help it attract and retain customers are the price of the item and the time taken to serve the customer. Based on the price for similar items in other neighboring restaurants, it is estimated that the customer tolerance limit for price is $8, and the associated customer loss is estimated to be $50. Similarly, the customer tolerance limit for the service time is 10 minutes for which the associated customer loss is $40. A random sample of size 10 yields the following values of price: 6.50, 8.20, 7.00, 8.50, 5.50, 7.20, 6.40, 5.80, 7.40, 8.30. The sample service times(in minutes) are 5.2, 7.5, 4.8, 11.4, 9.8, 10.5, 8.2, 11.0, 12.0, 8.5. Find the total expected loss per customer. If the restaurant expects 2000 customers monthly, what is the expected monthly loss

a) Total expected loss per customer = $31

b) Expected monthly loss = Expected loss on expected 2000 customers a month = $62,000

Step-by-step explanation:

random sample of size 10 yields the following values of price: 6.50, 8.20, 7.00, 8.50, 5.50, 7.20, 6.40, 5.80, 7.40, 8.30.

the customer tolerance limit for price is $8, and the associated customer loss is estimated to be $50.

Of the 10 samples, 3 of them exceed the customer tolerance limit for price ($8) and 7 of them stay in the limit.

For customers that stay in the limit, no customer loss,

But for customers that don't stay in the limit, there is a customer loss of $50.

E(X) = Σ xᵢpᵢ = 7(0) + 3(50) = $150.

On a per customer basis, E(X) = (150/10)

E(X) per customer = $15.

sample service times(in minutes) are 5.2, 7.5, 4.8, 11.4, 9.8, 10.5, 8.2, 11.0, 12.0, 8.5.

the customer tolerance limit for the service time is 10 minutes for which the associated customer loss is $40.

Of the sample of 10, 4 customers exceed the customer tolerance limit of 10 minutes and 6 stay in the limit.

For customers that stay in the limit, no customer loss,

But for customers that don't stay in the limit, there is a customer loss of $40.

E(X) = Σ xᵢpᵢ = 6(0) + 4(40) = $160

On a per customer basis, E(X) = (160/10)

E(X) per customer = $16.

Total expected loss per customer = $15 + $16 = $31

b) If the restaurant expects 2000 customers monthly, what is the expected monthly loss?

Expected loss per customer = $31

Expected losses on 2000 customers = 2000 × $31 = $62,000

Hope this Helps!!!

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probability for j is 1/4

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a is 1/6