Question

A normal distribution has a mean of 142 and a standard deviation of 16.

What is the probability that a randomly selected value lies between 142 and 174?

Answer 1

Mean = 142;
Standard Deviation ( "Sigma" ) = 16
172 = 142 + 32 = 142 + 2 * 16 = Mean + 2 Standard Deviation
It means that between 142 and 174 lies :
34 % + 13.5 % = 47.5 % of all values.
The probability that a randomly selected value lies between 142 and 174 is:
P = 0.475 

Answer 2

Let x be a random variable in the population.
P(142 < x < 174) = P((142 - 142)/16 < z < (174 - 142)/16) = P(0 < z < 2) = P(z < 2) - P(z < 0) = 0.97725 - 0.5 = 0.47725