The average playing time of compact discs in a large collection is 37 min, and t

Question

The average playing time of compact discs in a large collection is 37 min, and the standard deviation is 6 min. 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? Without assuming anything about the distribution of times, at least what percentage of the times are between 25 and 49 min? (Round the answer to the nearest whole number.) At least % Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 19 min or greater than 55 min? (Round the answer to the nearest whole number.) No more than % Assuming that the distribution of times is normal, approximately what percentage of times are between 25 and 49 min? (Round the answers to two decimal places, if needed.) % Less than 19 min or greater than 55 min? % Less than 19 min? %

Explanation / Answer

(d)

z-value for the time of 19min is: (19-37) / 6 = -3

z-value for the time of 55min is: (55-37) / 6 = 3

Less than 19min or greater than 55min:

Here we need to find the value : 1-(Area under normal distribution within 3 standard deviations from mean) = 1-(0.9973) = 0.0027 = 0.27%

For the next part, the answer is half of this, that is, 0.135%

These are the correct answers. Try entering '0.135' instead of just '.135' , and enter '0.27' instead of just '.27'

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