Question

For the following questions, assume that a randomly selected subject is given a bone density test. The test scores are normally distributed with a mean of 0, and a std. deviation of 1. Find the probability of the given bone density test scores. Round to 4 decimal places. (Hint- draw a graph to ensure you’re selecting the correct area (to left or right))

a. Less than -1.23

b. Greater than -2.00

c. Less than 2.56

d. Between 1.50 and 2.50

e. Between -4.27 and 2.34

f. Greater than 0

Answer 1

Solution:

We are given that the random variable follows standard normal distribution.

[All probabilities are calculated by using z-table or excel.]

Part a

P(Z<-1.23) = 0.1093

Part b

P(Z>-2) = 1 – P(Z<-2) = 1 - 0.02275 = 0.9773

Part c

P(Z<2.56) = 0.9948

Part d

P(1.50<Z<2.50) = P(Z<2.50) – P(Z<1.50) = 0.99379 - 0.933193 = 0.0606

Part e

P(-4.27<Z<2.34) = P(Z<2.34) – P(Z<-4.27) = 0.990358 – 0.00000977 = 0.9903

Part f

P(Z>0) = 1 – P(Z<0) = 1 – 0.5000 = 0.5000