Percentage grade averages were taken across all disciplines at a particular university, and the mean average was found to be 83.6 and the standard deviation was 8.7. If 18 classes were selected at random, find the probability that the class average is less than 80.A. 0.0235B. 0.7427C. 0.1730D. 0.0396

Correct Ans:
Option D

Solution.
This is a problem of statistics and uses the concepts of normal distribution. First step is to convert the given score into z score. 80 converted to z score for given mean, sample size and standard deviation will be:

[tex]z= \frac{80-83.6}{ \frac{8.7}{18} } =-1.756[/tex]

We are to find the probability that the class average is less than 80. Or in terms of z score, we have to find the score is less than -1.756. 

Using the standard normal distribution table this probability comes out to be 0.0396.

Therefore, the probability that the class average is less than 80 is 0.0396