Assume the student body of a large university (with over 10,000 students) is 55% female, 45% male. Fifteen students are selected randomly. Let X represent the number of females in the sample. (4 pts) Find the mean, variance, and standard deviation of X.

Mean = 8.25

Variance = 3.7125

Standard deviation = 1.927

Step-by-step explanation:

Let the probability of X be p.

Then

It follows that X is a binomial random variable.

For a binomial distribution, for n samples,

Mean,

Variance,

Standard deviation,

Using values in the question, n = 15

Mean =

Variance =

Standard deviation =

area = 13.8 cm²

Explanation:
The area of the triangle can be calculated using the following rule:
area of triangle = (1/2) * base * height

In the given:
base of triangle = 6.9 cm
height of triangle = 4 cm

Substitute with the givens in the above equation to get the area as follows:
Area = (1/2) * (6.9) * (4)
Area = 13.8 cm²

Hope this helps :)