The average playing time of compact discs in a large collection is 35 minutes, a

Question

The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 4 minutes. What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean? 1 standard deviation above the mean 1 standard deviation below the mean 2 standard deviations above the mean 2 standard deviations below the mean (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 27 and 43 minutes? (Round the answer to the nearest whole number.) At least (c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 23 minutes or greater than 47 minutes? (Round the answer to the nearest whole number.) No more than (d) Assuming that the distribution of times is normal, about what percentage of times are between 27 and 43 minutes? (Round the answers to two decimal places, if needed.) Less than 23 min or greater than 47 min? Less than 23 min?

Explanation / Answer

Answers with explanations to the question:

a.

35+4
35-4
35+8
35-8

b. Right, use Chebeshev' equality theorm for approx area = 1-1/2^2
c. Right, use Chebeshev' equality theorm for approx area = 1-(1-1/3^2)= 11%
d. Now, go to empirical formula for normal dist.

-means area within 1 devs away - 68%
-means area outside 2 devs away = 5%
-means area to the left of 2 devs left of mean = 5%/2 = 2.5%

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