Question

A statistical practitioner determined that the mean and standard deviation of a data set which is symmetrical and normal (bell-shaped) were 120 and 10, respectively. What can you say about the proportions of observations that lie between each of the following intervals?

a.   90 and 150

b. 100 and 140

c. 110 and 150

Answer 1

= 120, = 10

Here data set is symmetrical and normal (bell-shaped). Hence we are using empirical rule

as shown in following diagram.

a.   90 and 150

using empirical rule 99.7 % of data lie between 3 standard deviation from mean

hence, proportion of observations lie between  90 and 150 is = 0.9970

b. 100 and 140

using empirical rule 95 % of data lie between 2 standard deviation from mean

hence, proportion of observations lie between 100 and 140 is = 0.9500

c. 110 and 150

using above diagram we find that between  110 and 150 proportion of

observations lie = 34 %+ 34 %+ 13.5% + 2.35% = 83.85 %

proportion of observations lie between  110 and 150 is = 0.8385