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 i quadrupled. How will the standard deviation of sample mean printing speed change? A. It will decrease by a factor of 2. B. It will increase by a factor of 2. C. It will increase by a factor of 4. OD. 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 increase by a factor of 2. B. It will decrease by a factor of 2. C. It will increase by a factor of 4. D. It will decrease by a factor of 4. 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 an incorrect statement. The distribution of the mean printing speed of the sample is not Normal. B. It is a correct statement, but it is not a result of the Central Limit Theorem. C. It is a correct statement, and it is a result of the Central Limit Theorem.
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 i quadrupled. How will the standard deviation of sample mean printing speed change? A. It will decrease by a factor of 2. B. It will increase by a factor of 2. C. It will increase by a factor of 4. OD. 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 increase by a factor of 2. B. It will decrease by a factor of 2. C. It will increase by a factor of 4. D. It will decrease by a factor of 4. 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 an incorrect statement. The distribution of the mean printing speed of the sample is not Normal. B. It is a correct statement, but it is not a result of the Central Limit Theorem. C. It is a correct statement, and it is a result of the Central Limit Theorem.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text: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 decrease by a factor of 2.
B. It will increase by a factor of 2.
C. It will increase by a factor of 4.
OD. 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 increase by a factor of 2.
B. It will decrease by a factor of 2.
C. It will increase by a factor of 4.
D. It will decrease by a factor of 4.
E. It will remain unchanged.
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Part iii) Consider the statement: 'The distribution of the mean printing speed of the sampled printers is Normal.'
A. It is an incorrect statement. The distribution of the mean printing speed of the sample is not Normal.
B. It is a correct statement, but it is not a result of the Central Limit Theorem.
C. It is a correct statement, and it is a result of the Central Limit Theorem.
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