Question

The average playing time of compact discs in a large collection is 37 minutes, and the standard deviation is 3 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 31 and 43 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 28 minutes or greater than 46 minutes? (Round the answer to the nearest whole number.) No more than 이 (d) Assuming that the distribution of times is normal, about what percentage of times are between 31 and 43 minutes? (Round the answers to two decimal places, if needed.) Less than 28 min or greater than 46 min? % Less than 28 min? 이

Answer 1

We have given

Mean = 37 and SD = 3

Then

(a)

(1) one SD above the mean = mean + sd = 37+3 = 40

(2) one SD below the mean = mean - sd = 37-3 = 34

(3) two SD above the mean = mean + 2*sd = 37+6 = 43

(4) two SD below the mean = mean - 2*sd = 37 - 6 = 31

(b) 95%, because 2*SD below and above the mean is the 95% sample mean of the true population will lie between 31 and 43.

(c) 99.7% approximately 100%, because 99.7% CI is

Three SD above the mean = 37+3*3 = 37+9 = 46

Three SD below the mean = 37 - 3*3 = 37-9 = 28

(d) 95.30%

99.7%

68%