Question

the quality control manager at a factory records the number of equipment breakdowns each day. let the random variable ( y ) represent the number of breakdowns in one day. the standard deviation of ( y ) is 0.28. which of the following is the best interpretation of the standard deviation?

a. the number of breakdowns on a randomly selected day is expected to be 0.28.

b. the number of breakdowns on a randomly selected day will be 0.28 away from the mean.

c. the average number of breakdowns per day for a random sample of days is expected to be 0.28.

d. on average, the number of breakdowns per day varies from the mean by about 0.28.

Explanation:

Standard deviation measures the average amount that individual data points deviate from the mean of a dataset. Option A and C describe the mean, not standard deviation. Option B incorrectly states that every value will be exactly 0.28 from the mean, which is not true—standard deviation is an average deviation, not a fixed deviation for all points. Option D correctly captures that standard deviation represents the typical (average) variation from the mean.

Answer:

D. On average, the number of breakdowns per day varies from the mean by about 0.28.