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)

Answer 1

Answer)

N = 20

P = 0.35

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 7

N*(1-p) = 13

Both the conditions are met so we can use standard normal z table to estimate the probability

P(x<=5)

By continuity correction

P(x<5.5)

Z = (x - mean)/s.d

Mean = n*p = 7

S.d = √{n*p*(1-p)} = 2.13307290077

Z = (5.5 - 7)/2.13307290077

Z = -0.7

From z table, P(z<-0.7) = 0.2420