The average playing time of compact discs in a large collection is 33 minutes, a

Question

The average playing time of compact discs in a large collection is 33 minutes, and the standard deviation is 3 minutes. (a) 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 mean36 1 standard deviation below the mean30 2 standard deviations above the mean39 2 standard deviations below the mean 27 (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 27 and 39 minutes? (Round the answer to the nearest whole number.) At least 75 (c) Without assuming anything about the disribution of times, what can be said about the percentage of times that are either less than 24 minutes or greater than 42 minutes? (Round the answer to the nearest whole number.) No more than 11.11 (d) Assuming that the distribution of times is normal, about what percentage of times are between 27 and 39 minutes? (Round the answers to two decimal places, if needed) 0.95 Less than 24 min or greater than 42 min? 0.0027 % Less than 24 min? 0.00135 x%

Explanation / Answer

d) The percentage of time are between 27 and 39 minutes is nothing but 2SDs from the mean is 95.45%
since P(-2<Z<2) = 0.9545
Answer: 95.45%

P(x<24 or X>42) = P(X<24) + P(X>42)

= P(Z < (24-33)/3) + P(Z < (42-33)/3)
= P(Z<-3) + P(Z>3)
= 0.00135+0.00135 = 0.0027
Answer: 0.27%

P(X<24) = P(Z < (24-33)/3) = P(Z<-3) = 0.00135
Answer: 0.14%

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