Suppose that the probability of getting an A in a particular

Suppose that the probability of getting an A in a particular course is 0.08, and assume that the all student grades are independent. If you randomly sample 20 students taking the course

(a) Find the expected number of students that will get an A, and the standard deviation of number of students that will get an A.

(b) Find the probability that no student gets an A.

(c) Find the probability that at most 2 students get an A.

(d) Find the probability that between 2 and 4 students get an A.

Solution

Suppose that the probability of getting an A in a particular course is 0.08, and assume that the all student grades are independent. If you randomly sample 20 students taking the course

p=0.08

n=20

Expectation = np = 1.6

Variance = np(1 - p) = 1.472

Standard deviation = 1.21326

P(X=0) = (₂₀C₀) 0.08⁰ (1-0.08)^20-0   

P(X = 0) = 0.1887

P(x=0) =0.1887

P(x=1) = 0.3282

P(x=2) = 0.2711

P(x<=2) =0.1887+0.3282+0.2711 =0.788

P( 3<x<4) = P(x=3) = 0.1414