Question

The average playing time of compact discs in a large collection is 32 minutes, and the standard deviation is 4 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?

1 standard deviation above the mean | |

1 standard deviation below the mean | |

2 standard deviations above the mean | |

2 standard deviations below the mean |

(b) Without assuming anything about the distribution of times, at
least what percentage of the times are between 24 and 40 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
20 minutes or greater than 44 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 24 and 40 minutes? (Round the
answers to two decimal places, if needed.)

%

Less than 20 min or greater than 44 min?

%

Less than 20 min?

%

Answer #1

**ANSWER::**

**a)**

1 standard deviation above the mean -- 32+4 =36

. 1 standard deviation below the mean =32-4 =28

2 standard deviations above the mean 32+4*2 =40

2 standard deviations below the mean =32-4*2=24

**b)**

from Chebychev

percentage of the times are between 24 and 40 minutes(2 std deviation from mean) =(1-1/k2)*100

=(1-1/22)*100**=75%**

**c)**

percentage of times that are either less than 20 minutes or greater than 44 minutes =(1/k2)*100=(1/32)*100=11.0%

**d)**

FOR NORMAL distribution

percentage of times are between 24 and 40 minutes
**=99.45%**

Less than 20 min or greater than 44 min
**=0.27%**

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