Assuming a normal distribution with a true mean of 17 Inches

Assuming a normal distribution with a true mean of 17 Inches and a standard deviation of 0.21 Inches, what is the probability (in percentage) that future measurements will fall above 16.8 Inches?

Solution

u = mean = 17
Std-dev = SD = 0.21
x = 16.8

z = (x - u) / SD

z = (16.8 - 17) / 0.21

z = -0.95238

So, P(x > 16.8) = 1 - (0.17106)

0.82894

So, 82.89% approx