A design engineer wants to construct a sample mean chart for controlling the service life of one of the types of light bulbs his company produces.He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.On three recent production batches,he tested service life on random samples of four bulbs,with these results: What is the standard deviation of the sampling distribution of sample means?
A)5 hours
B)6.67 hours
C)10 hours
D)11.55 hours
E)20 hours

Question

A design engineer wants to construct a sample mean chart for controlling the service life of one of the types of light bulbs his company produces.He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.On three recent production batches,he tested service life on random samples of four bulbs,with these results:  What is the standard deviation of the sampling distribution of sample means?
A)5 hours 
B)6.67 hours 
C)10 hours 
D)11.55 hours 
E)20 hours

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of sample means is calculated using the formula:

Standard deviation of sample means (σx̄) = Standard deviation of population (σ) / √(sample size)

In this case, the standard deviation of the population (σ) is 20 hours and the sample size (n) is 4.

σx̄ = 20 / √4 = 10 hours

Therefore, the correct answer is (C) 10 hours.

A Design Engineer Wants to Construct a Sample Mean Chart