The average playing time of compact discs in a large collection is 33 minutes, a
ID: 3179813 • Letter: T
Question
The average playing time of compact discs in a large collection is 33 minutes, and the standard deviation is 2 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?
(b) Without assuming anything about the distribution of times, at least what percentage of the times are between 29 and 37 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 27 minutes or greater than 39 minutes?(Round the answer to the nearest whole number.)
No more than %
(d) Assuming that the distribution of times is normal, about what percentage of times are between 29 and 37 minutes? (Round the answers to two decimal places, if needed.)
%
Less than 27 min or greater than 39 min?
%
Less than 27 min?
%
Explanation / Answer
1
1 standard deviation above the mean =33+2=35
2)
standard deviation below the mean =33-2=31
3) 2 standard deviation above the mean =33+4=37
4)
standard deviation below the mean =33-4=29
b) as it lies 2 std deviation from mean hence from Tchebycheff's (1-1/22)*100 =75% values lies in them
c)as it lies outisde of 3 std deviation away hence (1/32)*100 =11.11% values fall outside of them
d)P(-2<Z<2) =95.45%
P(27>X & 39>X)= 1-P(-3<Z<3) =0.27%
less then 27 min =0.135%
1 standard deviation above the mean =33+2=35
2)
standard deviation below the mean =33-2=31
3) 2 standard deviation above the mean =33+4=37
4)
standard deviation below the mean =33-4=29
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