The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. Calculate the expected number of defects for a 1000-unit production.

A. 524.8
B. 742.1
C. 317.4
D. 500

C. 317.4

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Tthe process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

So

Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. Calculate the expected number of defects for a 1000-unit production.

The first step is finding the probability that a unit is defective.

This is

1 subtracted by the pvalue of Z when X = 10.15

has a pvalue of 0.8413

1 - 0.8413 = 0.1587

So

pvalue of Z when X = 9.85

has a pvalue of 0.1587

Probability of a unit being defective

Expected number for 1000

So the correct answer is:

C. 317.4

step-by-step :

so, converting firstly the mixed fractions to improper fractions and then "adding".