Question

1. Bone Density Test A bone mineral density test is used to identify a bone disease. The result of a bone density test is commonly measured as a z score, and the population of z scores is normally distributed with a mean of 0 and a standard deviation of 1.

a. For a randomly selected subject, find the probability of a bone density test score less than 1.54.

b. For a randomly selected subject, find the probability of a bone density test score greater than -1.54.

c. For a randomly selected subject, find the probability of a bone density test score between -1.33 and 2.33.

d. Find Q1, the bone density test score separating the bottom 25% from the top 75%.

e. If the mean bone density test score is found for 9 randomly selected subjects, find the probability that the mean is greater than 0.50.

Triola, Marc M.. Biostatistics for the Biological and Health Sciences (p. 277). Pearson Education. Kindle Edition.

Answer 1

1. The probability less than the Z score (or) the area of the normal curve to the left of Z score is obtained from the Standard Normal Table:

a. For Z less than 1.54:

= 0.93822

b.

= 1 - 0.06178

= 0.93822

= 0.93822

c.

= 0.99010 - 0.09176

= 0.89834

d. Q1, the bone density test score separating the bottom 25% from the top 75% would be that value whose area to the left is 0.25. Looking for the area 0.25 in the table:

The exact Z score would lie betwee -0.67 and -0.68.

Using the excel function:

Q1, the bone density test score separating the bottom 25% from the top 75% is -0.6745

e. Mean bone density test score found for 9 randomly selected subjects would also be in the form of a Z score with mean 0 and variance 1.

= 1 - 0.69146

= 0.30854