Assume a randomly selected subject is given a bone density test. Bone density te

Question

Assume a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. For each question, draw a graph, and find the result.

a. What is the probability the subject has a bone density score less than -0.19?

b. What is the probability the subject has a bone density score greater than 1.82?

c. What is the probability the subject has a bone density score between 1.23 and 2.37?

d. Find the bone density score that represents the 80th percentile.

Explanation / Answer

Solution :

Using standard normal table,

a) P(z < -0.19) = 0.4247

Probability = 0.4247

b) P(z >1.82) = 1 - P(z < 1.82) = 1 - 0.9656 = 0.0344

Probability = 0.0344

c) P(1.23 < z < 2.37) = P(z < 2.37) - P(1.23)

= 0.9911 - 0.8907

= 0.1004

Probability = 0.1004

d) P(Z < z) = 0.80

P( Z < 0.84) = 0.80

80th percentile = 0.84

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