A university has 10,000 students of which 55% are male and 45% are female. if a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students.

Question

Rebecca Moyer

Mathematics

3 January, 08:40

A university has 10,000 students of which 55% are male and 45% are female. if a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students.

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Susannah · Answer 1

Information provided:

Sample size, n = 30 students

P (Male), P (m) = 55% = 0.55

P (Female), P (f) = 45% = 0.45

Now,

Mean = nP (m) = 30*0.55 = 16.5 ≈ 17 students

Variance = (sd) ^2 = nP (m) P (f) = 30*0.55*0.45 = 7.425 ≈ 8 students