The average playing time of compact discs in a large collection is 34 minutes, a

Question

The average playing time of compact discs in a large collection is 34 minutes, and the standard deviation is S 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 39 1 standard deviation below the mean 29 2 standard deviations above the mean 44 2 standard deviations below the mean 24 (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 24 änd 44 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 19 minutes or greater than 49 minutes? (Round the answer to the nearest whale number:) No more than [ ] % 44 mi wers to two decimal places, if needed.) Less than 19 min or greater than 49 min? Less than 19 min?

Explanation / Answer

Solution:-

b) 24 = - ks = 34 - 2*5

44 = + ks = 34 + 2*5

k = 2

1 - (1 / (k^2))

= 1 - 1/4

= 0.75

= 75 %

c) k = 3 There fore  49 = + ks = 34 + 3*5

= (1 / (k^2))

= 1/9

= 0.11

= 11%

d) P(24 < X < 44) = P((24 - 34)/5 < Z < (44 - 34)/5)

= P(-2 < Z < 2)

= 0.9544

= 95.44%

=> P(Z < -3) + P(Z < 3)

= 0.0013 + 0.0013

= 0.0026

= 26%

=> P(X < 19) = P(Z < -3) = 0.0013 = 0.13%

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