Question

In an undergraduate computer science program, 35% of the students are women. At a recent invitation-only hackathon, 5 of the 20 students selected to participate were female. Are females being underrepresented here? To find out if this occurrence is unusual and warrants more investigation, calculate the probability of the current situation or something more extreme. In other words, calculate the probability that 5 or fewer female students are chosen based on the proportion of females in the program. Does the occurrence seem unusual to you? (Write out the formula, and then use Excel to calculate the probability.)

Answer 1

Here x = Number of female participants in an undergraduate computer science program.

n = 20 , p = 0.35

If p (X < = 5 ) is less than 0.5 then we can say that this occurrence is unusual and warrants more investigation .Because ther is equal chance (0.5) of occurrence for males and females.

We find p (X < = 5 ) in excel by using following function :

=BINOMDIST(5,20,0.35,TRUE) = 0.2454

This probability is less than 0.5, hence this occurrence is unusual and warrants more investigation.