The performance of students is given by the following result:
52,74,54,12,47,36,48,84,65,42,15,45,74,36,
47,53,57,32,41 and 58.
If the pass mark is 50. What is the probability that a student should score 84?
To figure the probability, the pass mark is extraneous information, not needed.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
I'll let you do the calculations.