My Notes Ask Your Teacher The average playing time of compact discs in a large c

Question

My Notes Ask Your Teacher The average playing time of compact discs in a large collection is 32 min, and the standard deviation is 3 min. (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? standard deviation above 35 the mean 1 standard deviation below the mean 29 2 standard deviation above the mean 38 2 standard deviation below 2 e mean (b) Without 38 min? (Round the answer to the nearest whole number.) At least assuming anything about the distribution of times, at least what percentage of the times are between 26 and (e) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 23 min or greater than 41 min? (Round the answer to the nearest whole number.) No more than (d) Assuming that the distribution of times is normal, approximately what percentage of times are between 26 and 38 min? (Round the answers to two decimal places, if needed.) Less than 23 min or greater than 41 min? Less than 23 min? Practice Another Version Submit Answer Save Prog

Explanation / Answer

Answer:

b). 95% ( 2 standard deviations limits)

c). 99% ( 3 standard deviations limits)

d).

z value for 26 , z=(26-32)/3 =-2

z value for 38 , z=(38-32)/3 =2

P( 26<x<38)= P( -2<z<2) =P( z <2)-P( z <-2)

= 0.9772- 0.0228=0.9544

=95.44%

P( x < 23 or x >41) = P( z<-3 or z > 3) = 0.0013+0.0013 = 0.0026

=0.26%

P( x <23) = P( z < -3)=0.0013

=0.13%

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