Question

The mean playing time for a large collection of compact discs is 37 minutes, and the standard deviation is 4 minutes.

(a)

What value (in minutes) is 1 standard deviation above the mean?

One standard deviation below the mean?

What values are 2 standard deviations away from the mean?

1 standard deviation above the mean  min

1 standard deviation below the mean  min

2 standard deviations above the mean  min

2 standard deviations below the mean  min

(b)

Assuming that the distribution of times is mound-shaped and approximately symmetric, approximately what percentage of times are between 29 and45 minutes? (Hint: See Example 3.19. Use the Empirical Rule.)

Less than 25 min or greater than 49 min?

Less than 25 min?

Answer 1

a) The value (in minutes) is 1 standard deviation above the mean

= 37 + 4

= 41

The value (in minutes) is 1 standard deviation below the mean

= 37 - 4

= 33

The value (in minutes) is 2 standard deviation above the mean

= 37 + (2*4)

= 45

The value (in minutes) is 2 standard deviation below the mean

= 37 - (2*4)

= 29

b) Since the distribution of times is mound-shaped and approximately symmetric,

Using empirical rule, we know 95.45% values lie between (mean - 2*standard deviation, mean + 2*standard deviation)

So,  95.45% values lie between (29, 45)

So, (100 - 95.45) = 4.55% values lie outside the interval (29, 45),i.e. either less than 25 min or greater than 49 min.

and values will be less than 25 min.