Question

Serum glutamic oxaloacetic transaminase (SGOT) is an enzyme that elevates when the heart muscle is damaged. Assume that the population distribution of SGOT levels in adults with healthy hearts is known to be normally distributed with mean = 18.7 μg/L and standard deviation = 3.9 μg/L.

1. How likely is it that a single adult with a healthy heart has an SGOT level of above 20 units/L?

2. Now suppose you collected a sample of n = 50 adults who recently underwent heart surgery. What is the probability that the average of those 50 adults has an SGOT level above 20 units/L?

Answer 1

1. Let X be the SGOT level

then

To find P( X> 20 )

= P( z > 0.33)

= 0.3821 (from z table : area from 0.33 to )

2.

Let be the average SGOT level of 50 adults  

with mean = 18.7 and standard error =

Then

= P( z > 2.36 )

= 0.0093    (from z table : area from 2.36 to )