The average playing time of compact discs in a large collection is 32 minutes, a

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?

Explanation / 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%

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.