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 negative 1.15−1.15 and draw a sketch of the region.

Step-by-step explanation:

Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 0

σ = 1

the probability that a given score is less than negative 1.15 is expressed as

P(x < - 1.15)

z = (- 1.15 - 0)/1 = - 1.15

Looking at the normal distribution table, the probability corresponding to the z score is 0.13

P(x < - 1.15) = 0.13

The sketch of the region is shown in the attached photo