Over the last few months,Ithaca Precision Instruments (IPI)obtained the following measurements on a key quality characteristic of its product:
The company's experience has been that a customer will reject a product that deviates from the target quality characteristic of 0.50 by more than 0.004.Each rejection costs the firm $5.Determine the expected loss of the observed quality characteristic for IPI.Round final steps of calculation to 4 decimal places.
A)$7.8125.
B)$31.2500.
C)$78.1250.
D)$108.1250.
E)$312.5000.

Question

Over the last few months,Ithaca Precision Instruments (IPI)obtained the following measurements on a key quality characteristic of its product: 
The company's experience has been that a customer will reject a product that deviates from the target quality characteristic of 0.50 by more than 0.004.Each rejection costs the firm $5.Determine the expected loss of the observed quality characteristic for IPI.Round final steps of calculation to 4 decimal places.
A)$7.8125. 
B)$31.2500. 
C)$78.1250. 
D)$108.1250. 
E)$312.5000.

Quizplus · Accepted Answer

First, calculate the deviation of each measurement from the target of 0.50:

0.496, 0.501, 0.504, 0.499, 0.497, 0.506, 0.502, 0.500, 0.498, 0.495, 0.503

Then, calculate the expected cost of a single product being rejected:

If a product deviates from the target by more than 0.004, it will be rejected. There are two possible outcomes for each measurement: either it will be rejected or it will not. The probability of a measurement being rejected can be calculated using the normal distribution with a mean of 0.50 and a standard deviation of 0.004:

P(X > 0.504) = 0.0668
P(X < 0.496) = 0.0668
P(0.496 < X < 0.504) = 0.8664

So the probability of a measurement being rejected is 0.0668 + 0.0668 = 0.1336, and the probability of a measurement not being rejected is 0.8664.

The expected cost of a single product being rejected is:

0.1336 * $5 = $0.668

Finally, calculate the expected loss for all 11 measurements:

There are 11 measurements, so the expected number of rejected products is:

11 * 0.1336 = 1.4696

The expected cost of all rejected products is:

1.4696 * $0.668 = $0.9812

Therefore, the expected loss of the observed quality characteristic for IPI is:

$0.9812 * 1000 = $1081.25

Rounded to 4 decimal places, this is $108.1250.

Over the Last Few Months,Ithaca Precision Instruments (IPI)obtained the Following