Question

The probability for receiving an A in Calculus is given to be 20% in a class of 1000. If 20 students are chosen (with replacement) from the class, what is the probability that five of them received A’s? Round to the nearest four decimal places.

Answer 1

Here, n = 20, p = 0.2, (1 - p) = 0.8 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 5)
P(X = 5) = 20C5 * 0.2^5 * 0.8^15
P(X = 5) = 0.1746