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?

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

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