Error Rate

[VIGNESHWARR]

In 1995 division A of Company X had 4850 customers.If there were 86 service errors in division A that year,what was the service-error rate,in number of service errors per 100 customers, for Division B of company X in 1995.

1.in 1995 the overall service-error rate for division A and B was 1.5 service errors per 100 customers.

2.In 1995 Division B had 9350 customers,none of whom were customers of Division A.

[fcabanski]

This is a rate problem:

A = Rate/100 = #ErrorsA/#CustomersA * 100
B = Rate/100 = #ErrorsB / #CustomersB * 100

Combined Rate = (ErrorsA + ErrorsB)/ (CustomersA+CustomersB) * 100

Error rate for A (per 100) is 86/4850 * 100 = appox. 1.77 errors per 100 customers.

What information is needed to answer the question?

- number of errors for B and number of customers for B.
- some statement of the relationship of service errors for B to service errors for A.

Statement 1- in 1995 the overall service-error rate for division A and B was 1.5 service errors per 100 customers.

It doesn't tell us what number of people were customers of Division B. We know the rate must be less than 1.5 since the A rate is 1.77, but without knowing the number of B customers the B rate could be many different things. The more B customers, the more weight the B error rate has in the overall AandB rate, so the higher the B rate can be.

For example, if there are 1,000,000,000 B customers, the A customers and A error rate become meaningless. If the B rate is 1.5 then the overall rate is 1.5 because B carries so much weight.

But if there are only 1000 B customers, then the A rate still matters. The B rate has to be very low to pull the overall rate down from 1.77 to 1.5.

Insufficient. Eliminate A and D. The possible answers are B, C or E.

Statement 2: In 1995 Division B had 9350 customers,none of whom were customers of Division A.

This tells us nothing about the overall (A and B) error rate, or the errors for B, or the error rate for B.

Insufficient. Eliminate B. The possible answers are C and E.


Statement 1 plus Statement 2:

Statement 1 relates the combined rate (ErrorsA + ErrorsB)/ (CustomersA+CustomersB) * 100 = 1.5
Statement 2 relates the number of B customers (9350.)

Both together would allow us to find the number of B errors, and thus the B error rate.

1 and 2 together are sufficient. Eliminate E. The answer is C.

(86 + ErrorsB)/ (4850+9350) * 100 = 1.5

(86 + ErrorsB)/ (4850+9350) = .015
86 + Errors B = .015 * 14200 = 213

Errors B = 213 - 86 = 127

B rate per 100 = 127/9350 * 100 = appox. 1.36