Let x be a random variable representing the number of female students enrolled in the university. This is a binomial distribution since there are two outcomes only. The student is either a male or a female
From the information given. the probability that the student is a female is
53/100 = 0.53
Thus, p = 0.53
The probability that the student is not a female, q is 1 - p
Thus, q = 1 - 0.53 = 0.47
a) We want to determine the probability of P(x = 20)
Given that n = 32, from the binomial distribution table,
p(x = 20) = 0.08
the probability that 20 of the students sampled are female is 0.08
b) Half of the sample is 32/2 = 16. The probability that less than half of the sample is a female is expressed as
p(x < 16) = 0.3
the probability that less than half of the sample is female is 0.3