SOLUTION: If you solve the question below, I'll be appreciated. An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells y

Question 1205516: If you solve the question below, I'll be appreciated.
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 17.08 ppm and a standard deviation of 4.5 ppm. Suppose that you draw a random sample of 12 printers.
Part i) Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 17.18 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
Probability (as a proportion) ?
Part ii) Use normal approximation to find the probability that more than 44.9% of the sampled printers operate at the advertised speed (i.e. the printing speed is equal to or greater than 18 ppm)
A. 0.5070
B. 0.5834
C. 0.4930
D. 0.4166
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
answer to part 1 is equal to .469 rounded to 3 decimal places.

here's what it looks like on a normal distribution graph.

using my calculator, i got .4694 rounded to 4 decimal places.
the difference between my calculations and the normal distribution calculator was due to rounding.
i rounded intermediate results to 4 decimal places.
the calculator didn't do any intermediate rounding except for the standard error which i rounded to 4 decimal places before entering.

the standard error had to be used because you were looking for the mean of the sample rather than the value of a single element in the population.

i don't understand what they are looking for in part 2.

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