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

Probability that a randomly selected value lies between `142` and `174` is `0.47725`.

Explanation:

`z`-score for a normal distribution with mean as `mu` and standard deviation as `sigma` is given by `(x-mu)/sigma`

In the given distribution, mean is `142` and standard deviation is `16`

the `z`-score for value at `142` is `(142-142)/16=0` and

`z`-score for value at `174` is `(174-142)/16=32/16=2`

from the tables probability associated with range of `z`-score from `142` to `174` is `0.47725`.