Question

The distribution of rhesus monkey tail lengths can be approximated by N(6.8, 0.44). Both mean and standard deviation are given in centimeters. What is the cutoff value for the 80th percentile. In other words, 80% of tail lengths are less than what value?

Answer 1

7.17 cm

Explanation:

Given that :

Mean (m) = 6.8 cm

Standard deviation (s) = 0.44 cm

Cut off value for the 80th percentile :

The cut off value :

From ;

Zscore = (x - m) / s

x = cut off value

Zscore corresponding to 80%(0.8) = 0.842 (from z probability calculator)

Plugging into our formula :

0.842 = (x - 6.8) / 0.44

0.842 * 0.44 = x - 6.8

0.37048 = x - 6.8

0.37048 + 6.8 = x

7.17048 = x

X = 7.17 cm