Question

For a symmectric bell shaped population with a mean of 20 and a standard deviation of 3 find the following.

a) Use the empirical rule to find the interval that contain about 99.7% of all the values

b) what is the z-score of an observation, 30 under this distribution

c) is 30 an outlier in this data set

d) give the evidence for your answer in part c

Answer 1

Answer : mean = 20 , standard deviation = 3

A) according to empirical rule, 99.7% values lies within 3 standard deviation of the mean. So the interval is : ((20-3*3), (20+3*3)) = (11,29)

B) z = (30 - mean) / sd = (30-20)/3 = 10/3 = 3.3334

C) yes 30 is an outlier, as the z score of 30 is greater than 3 it means the point is more than 3 standard deviations away from the mean hence can be considered as outlier.

D) explained above + 99.7% data lies within 3 standard deviation from the mean. The remaining 0.3% can be considered as outlier.