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 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 mean 38 1 standard deviation below the mean 32 2 standard deviations above the mean41 2 standard devlations below the mean 29 (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 29 and 41 minutes? (Round the answer to the nearest whole number) At least 95 () Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 26 minutes or greater than 44 minutes? (Round the answer to the nearest whole number.) No more than o (d) Assuming that the distribution of times is normal, about what percentage of times are between 29 and 41 minutes? (Round the answers to two decimal places, if needed.) Less than 26 min or greater than 44 min? Less than 26 min? 15

Explanation / Answer

Ans:

mean=35

standard deviation=3

b)29 and 41 are 2 standard deviations away from mean.

Using Cheybev's therom:

k=2

1-(1/k^2)=1-(1/2^2)=1-(1/4)=3/4=0.75

75% is the correct answer.

c)26 and 44 are 3 standard deviations away from mean.

k=3

1-(1/k^2)=1-(1/3^2)=1-(1/9)=8/9=0.89

Atleast 89% liw between 26 and 44,so no more than 11% lie outside 26 and 41.

11% is the correct ansqwer.

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