Answer to Question #269252 in Statistics and Probability for icaaa

Question

A certain experiment conducted was normally distributed. The mean value is 50 and the standard deviation is 4. If the total population is 1000 (discrete variable), calculate the probability for getting an x-value greater than 45

Answer 1

$\mu=50, \sigma=4, N=1000$

We need to find the probability for getting an x-value greater than 45 given as,

$p(X\gt 45)$ and since the experiment conducted was normally distributed, we shall standardize and use the standard normal tables to obtain its value as follows

$p(X\gt45)=p((X-\mu)/\sigma\gt(45-\mu)/\sigma)=p(Z\gt (45-50)/4)=p(Z\gt-1.25)$

This probability is equivalent to,

$p(Z\gt-1.25)=1-p(Z\lt-1.25)=1-0.1056=0.8944$

Therefore,  the probability for getting an x-value greater than 45 is 0.8944.