Question

Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen. d. How many are expected to attend their graduation? e. Find the probability that 17 or 18 attend. f. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.

Answer 1

This is a binomial distribution with n = 22 and p = 0.85

d) E(x) = n*p = 22*0.85 = 18.7 students are expected to attend their graduation.

e) P(17 or 18) = P(17) + P(18)

Hence, 0.3249 (rounded to 4 decimal places) is the probability that 17 or 18 will attend.

When the probability of any event is less than 0.05 then that's an ususual event.

Here probability that all 22 will attend is 0.028 which is less than 0.05, hence I will be surprised if all 22 attend the graduation.

Please comment if any doubt. Thank you.