The average playing time of compact discs in a large collect

The average playing time of compact discs in a large collection is 32 min, and the standard deviation is 6 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?

(b) Without assuming anything about the distribution of times, at least what percentage of the times are between 20 and 44 min? (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 14 min or greater than 50 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 20 and 44 min? (Round the answers to two decimal places, if needed.)
%
Less than 14 min or greater than 50 min?
%
Less than 14 min?
%

Solution

(a) About 68% of the area under the normal curve is within one standard deviation of the mean. i.e.                                  
(u ± 1s.d)                                  

1 standard deviation above the mean   38
1 standard deviation below the mean   26

About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)

2 standard deviation above the mean   44
2 standard deviation below the mean   20
d)
i)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 20) = (20-32)/6
= -12/6 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 44) = (44-32)/6
= 12/6 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(20 < X < 44) = 0.97725-0.02275 = 0.9545                  

ii)
To find P( X > a or X < b ) = P ( X > a ) + P( X < b)
P(X < 14) = (14-32)/6
= -18/6= -3
= P ( Z <-3) From Standard Normal Table
= 0.0013
P(X > 50) = (50-32)/6
= 18/6 = 3
= P ( Z >3) From Standard Normal Table
= 0.0013
P( X < 14 OR X > 50) = 0.0013+0.0013 = 0.0027                  

iii)
P(X < 14) = (14-32)/6
= -18/6= -3
= P ( Z <-3) From Standard Normal Table
= 0.0013