playing time of compact discs in a large standard 1 standard deviation above the

Question

playing time of compact discs in a large standard 1 standard deviation above the mean 34 1 standard deviation below the mean 30 2 standard deviations above the mean 3 2 standard deviations below the mean 28 uming anything about the distribution of times, at least what percentage of the times are between 28 and 36 minutes? (Round the answer to the nearest whole number) At least 90 (e) without assuming anything about the distribution of times, what can be said about the percentage of times that are et greater than 38 minutes? (Round th of times, what can be said about the percentage of times that are either less than 26 minutes or answer to the nearest whole number) No more than 16 (d) Assuming that the distribution of times is normal, about what percentage of times are between 28 and 36 minutes? (Round the answers to two decimal places,it needed ) Less than 26 min or greater than 38 min?

Explanation / Answer

mean= 32 minutes and standard deviation is 2 minutes

b) question is asking above 2 standard deviation and below 2 standard deviation so according to emperical rule at least 95% of the times are between 28 and 36 minutes.

c) either less than 26 or more than 38 is 0.13%

d) Since =32 and =2 we have:

P ( 28<X<36 )=P ( 2832< X<3632 )=P ( (2832)/2<(X)/<(3632)/2)

Since Z=(x)/ , (2832)/2=2 and (3632)/2=2 we have:

P ( 28<X<36 )=P ( 2<Z<2 ) Use the standard normal table to conclude that:

P ( 2<Z<2 )=0.9544= 95.44%

e) less than 26 min

Since =32 and =2 we have:

P ( X<26 )=P ( X<2632 )=P ((X)/<(2632)/2)

Since (x)/=Z and (2632)/2=3 we have:

P (X<26)=P (Z<3)

Use the standard normal table to conclude that:

P (Z<3)=0.0013= 0.13%

more than 38 min

Since =32 and =2 we have:

P ( X>38 )=P ( X>3832 )=P ( X>38322)

Since Z=(x)/ and (3832)/2=3 we have:

P ( X>38 )=P ( Z>3 )

Use the standard normal table to conclude that:

P (Z>3)=0.0013= 0.13%

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