The average playing time of compact discs in a large collection is 35 minutes, a

ID: 3304818 • Letter: T

Question

The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes.

a) What value is 1 standard deviation above the mean?

b) What value is 1 standard deviation below the mean?

c) What is the value 2 standard deviations above the mean?

d) What is the value 2 standard deviations below the mean?

e) What is the value 3 standard deviations above the mean?

f) What is the value 3 standard deviations below the mean?

g) Assuming that the distribution is approximately normal, about what percentage of times are between 30 and 40 minutes?

h) Assuming that the distribution is approximately normal, about what percentage of times are between 25 and 45 minutes?

i) Assuming that the distribution is approximately normal, about what percentage of times are less than 20 minutes or greater than 50 minutes?

j) Assuming that the distribution is approximately normal, about what percentage of times are greater than 50 minutes?

The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes.

a. 1 deviation above mean = Mean +1*sigma = 35+5 = 40

b. 1 deviation below mean = Mean -1*sigma = 35-5 = 30

c. 2 deviation above mean = Mean +2*sigma = 35+2*5=45

d. 2 deviation below mean = Mean -2*sigma = 35-2*5=25

e. 3 deviation above mean = Mean +3*sigma = 35+3*5=50

f. 3 deviation below mean = Mean -3*sigma = 35-3*5=20

h. P( 25<X<45) = P( -2<Z<2) = .95

i. P( X<20 and X>50) = .0013+.0013=.0026

j. P( X>50) = .0013

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