Question

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.

Answer 1

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.