What is the probability that X is greater than 113.88?

Question

Suppose that X is normally distributed with; mean = 90 and standard deviation = 12. 

What is the probability that X is greater than 113.88? 

Probability = ___

Answer 1

Pr(x>113.88) = ?

mean =90

sd = 12

z score = 113.88-90)/12 = 23.88/12 = 1.99 = almost 2, Probability of larger than 2 standard deviations above the mean, by the empirical rule, is (100-95)/2 = 5/2 = 2.5%

use a z calculator or z tables to get a more accurate percentage, 2.33%