Answer:
32% probability of a defect.
The expected number of defects for a 1000-unit production run is 320.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 10
Standard deviation = 0.15.
Probability of a defect
Weights less than 9.85 oz or greater than 10.15 oz will be classified as defects.
9.85 = 10 - 0.15
10.15 = 10 + 0.15
By the Empirical Rule, 68% of weights are between 9.85 and 10.15, that is, within the limits. 32% are not within the limits.
So there is a 32% probability of a defect.
Expected number of defects for a 1000-unit production run.
E(X) = 0.32*1000 = 320
The expected number of defects for a 1000-unit production run is 320.
