A sample data set has a mean of 57 and a standard deviation

A sample data set has a mean of 57 and a standard deviation of 15. Determine whether each of the following sample measurements are outliers.

a. 111

b. 47

c. 63

d. 49

Solution

About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.  
(u ± 2*s.d), the remaining 5% that are outside this range to be outliers.
u = 57, s.d= 15
(u ± 2*s.d) = ( 57 - 30, 57 + 30 ) = (27, 87) , each of the value is in between this range except 111

[ANSWER]

a. 111