Assume that a randomly selected subject is given a bone density test. those test scores are normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a given score is less than 1.66 and draw a sketch of the region.

Given:

μ = 0, the population mean

σ = 1, the population standard deviation

For the random variable x = 1.66, the z-score is

z = (1.66 - 0) / 1 = 1.66

From standard tables,

P (x < 1.66) = 0.952

Answer:

0.952 or 952%

The area (probability) is shown in the figure.