Question

Please determine the 83rd percentile of X.

32. Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 15.0 kips and standard deviation 1.25 kips. Compute the following probabilities by standardizing and then using Table A.3.

Answer 1

Solution:-

Given that,

mean = $\mu$ = 15.0

standard deviation = $\sigma$ = 1.25

Using standard normal table,

P(Z < z) = 83%

= P(Z < z) = 0.83  

= P(Z < 0.95) = 0.83

z = 0.95

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 0.95 * 1.25 + 15.0

x = 16.19