Question

A NUMMI assembly line, which has been operating since 1984, has built an average of 6,000 cars and trucks a week. Generally, 10% of the cars were defective coming off the assembly line. Suppose we draw a random sample of n = 100 cars. Let X represent the number of defective cars in the sample. What can we say about X in regard to the 68-95-99.7 empirical rule (one standard deviation, two standard deviations, and three standard deviations from the mean are being referred to)? Assume a normal distribution for the defective cars in the sample.

a) Most likely, X will be within 1 standard deviation of the mean.
b) It's impossible for X to be within 2 standard deviations of the mean.
c) X will be within 3 standard deviations of the mean 99.7% of the time.
d) X will never deviate from the mean by more than 1 standard deviation.

Answer 1

According to the empirical rule, X will most likely be within 1 standard deviation of the mean.

Step-by-step explanation:

The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. In the given problem, X represents the number of defective cars in a sample of 100 cars. Since we assume a normal distribution for the defective cars in the sample, we can apply the empirical rule to estimate the range of X:

a) Most likely, X will be within 1 standard deviation of the mean.

So, the correct answer is option a) Most likely, X will be within 1 standard deviation of the mean.