Question

At a large Midwestern college, 4 % 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X X denote the number of Hispanics among them. The standard deviation of X X is:______. a) 0.88. b) 0.8. c) 0.768. d) 0.71

Answer 1

Answer:

option a

Step-by-step explanation:

given that at a large Midwestern college, 4 % 4% of the students are Hispanic.

A  random sample of 20 students from the college is selected.

We have each student is independent of the other to be hispanic

p = success = being hispanic = 0.04 while

q = failure = being non hispanic = 0.96

X - no of hispanics is thus binomial with p = 0.04 and n =20 (sample size)

Since X is binomial

Var(x) = npq = 0.768

Std dev (x) = Square root of variance = $\sqrt{0.768} \\=0.8764$

rounded off it gives 0.88

So option a is right