Answer to Question #269243 in Statistics and Probability for Honey

Question

A certain experiment conducted was normally distributed. The mean value is 100.6725 and the standard deviation is 12.45. If the total population is 2000 (continuous variable), calculate the amount of population falling below an x-value of 120.75.

Answer 1

Let X be a random variable represents the result of an experiment, then X ~ $N(100.6725, 12.45^2) = 100.6725+12.45N(0, 1)$ $P(X<120.75)=P(100.6725+12.45N(0,1)<120.75)=P(N(0,1)<1.613)=0.94663$

So, for 2000 experiments we should expect that 2000*0.94663 = 1893.26, or 1893 if round, results falling below value 120.75