Question

Scores on an exam are normally distributed with expected value 70 and standard deviation 5. The Interquartile range of the distribution of this exam is, approximately, (a) 5.9 (b) 20 (c) 73 (d) 9 (e) 6.75

Answer 1

Here we have :

Mean = 70

Standard deviation = 5

Interquartile range IQR = Q3 - Q1

where Q1 and Q3 are at 25th and 75th percentile.

for 25 and 75th percentile; z = -/+0.6745

25th percentile Q1 = mean +z*std deviation = 70-0.6745*5 = 66.628

75th percentile Q3 = mean +z*std deviation = 70+0.6745*5 = 73.372

hence,

IQR = Q3 - Q1 = 73.372 - 66.628 = 6.75

Correct option "E"

6.75