Question

A college reported that 40% of its population is male. Nine students are selected at random The mean is Answer .The standard deviation is . (Round to the nearest hundredth, if necessary.) The shape of the distribution is

Answer 1

Explanation:

This is a binomial distribution because there are only two possible outcomes. It is either a randomly selected student is a male or a female. In this scenario, the probability of success, p is that a randomly selected student is a male and it is the same for any given number of trials. Therefore,

p = 40/100 = 0.4

The probability of failure, q would be that a randomly selected student is a female.

q = 1 - p = 1 - 0.4 = 0.6

Number of trials, n = 9

Therefore,

Mean = np = 9 × 0.4 = 3.6

Standard deviation = √npq = √9 × 0.4 × 0.6 = 1.47

The shape of the distribution is asymmetric.