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 1.77 and draw a sketch of the region.
sketch the region. choose the correct graph below.
a.
b.
c.
d.

Explanation:

Step1: Analyze the z - score range

We are looking for the region where the score is less than \(1.77\). In a standard normal distribution (symmetric about \(z = 0\)), the region to the left of \(z=1.77\) is what we need.

Step2: Eliminate wrong - graph options

• Option A: The region in option A is between \(z=-1.77\) and \(z = 1.77\), which is not the region we want (we want \(z<1.77\)).
• Option C: The region in option C is to the left of \(z=-1.77\), which is incorrect.
• Option D: The region in option D is to the left of \(z = 1.77\) but has a very small non - shaded part. However, when we consider the standard normal curve, the entire area to the left of \(z = 1.77\) should be shaded. Option B correctly represents the region to the left of \(z = 1.77\) in a standard normal distribution curve.

Answer:

B.