Question 1138477: An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.57 ppm and a standard deviation of 3 ppm. Suppose that you draw a random sample of 11 printers.
Part i) Suppose the number of printers drawn is quadrupled. How will the standard deviation of sample mean printing speed change?
A. It will increase by a factor of 4.
B. It will decrease by a factor of 2.
C. It will increase by a factor of 2.
D. It will decrease by a factor of 4.
E. It will remain unchanged.
Part ii) Suppose the number of printers drawn is quadrupled. How will the mean of the sample mean printing speed change?
A. It will decrease by a factor of 4.
B. It will increase by a factor of 4.
C. It will decrease by a factor of 2.
D. It will increase by a factor of 2.
E. It will remain unchanged.
Part iii) Consider the statement: 'The distribution of the mean printing speed of the sampled printers is Normal.'
A. It is a correct statement, and it is a result of the Central Limit Theorem.
B. It is a correct statement, but it is not a result of the Central Limit Theorem.
C. It is an incorrect statement. The distribution of the mean printing speed of the sample is not Normal.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If the sample size is quadrupled, the sd of the mean will decrease by a factor of sqrt (4), or 2. B
The sample mean will not change E
If the underlying distribution is known to be normal, the sampling distribution of the sample mean will be normal as well. The CLT is not needed unless one is sampling from a non-normal distribution. B
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