Question

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. 0.0235



B. 0.7427



C. 0.1730



D. 0.0396

Answer 1

The probability that the class average is less than 80 is found by calculating the Z-score and then referring to a Z-table or using a calculator. The Z-score for a class average of 80 with a mean of 83.6, standard deviation of 8.7, and sample size of 18 classes is -1.24, which corresponds to a probability of 0.1730 or 17.30%.

Step-by-step explanation:

The question deals with finding the probability that the class average is less than 80, given that the overall mean average is 83.6 and the standard deviation is 8.7. To find the probability, we should use the Z-score formula, which is Z = (X - μ) / (σ/√N), where X is the value of interest (80), μ is the mean (83.6), σ is the standard deviation (8.7), and N is the number of samples (18). The Z-score describes how many standard deviations the value of interest is from the mean.

The calculated Z-score is:

Z = (80 - 83.6) / (8.7/√18) = -1.24

Using a Z-table or a calculator, we find the probability corresponding to the Z-score of -1.24. This gives us the probability that one class average is less than 80.

The correct answer is C. 0.1730, which corresponds to the probability associated with the Z-score of -1.24. Therefore, there is a 17.30% chance that the average of a randomly selected class will be less than 80.

Answer 2

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:


`z= (80-83.6)/( (8.7)/(18) ) =-1.756`

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