Question

The average grade in a statistics course has been 70 with a standard deviation of 8. If a random sample of 51 is selected from this population, what is the probability that the average grade is more than 72? Use Appendix B.1 for the z-values. (Round your z-value to 2 decimal places and the final answer to 4 decimal places.) Probability

Answer 1

Solution:
Given in the question
Mean () = 70
Standard deviation() = 8
Number of sample (n) = 51
We need to calculate the probability that the average grade is more than 72 i.e. P(X>72) = 1- P(X<=72)
Here we will use standard normal distribution, First we will calculate Z-score which can be calculated as
Z-score = (X - )//sqrt(n) = (72-70)/8/sqrt(51) = 2/1.12 = 1.79
From Z table we found p-value
P(X>72) = 1 - P(X<=72) = 1 - 0.9633 = 0.0367
So there is 3.67% probability that the average grade is more than 72.