Each question is a sentence about a count. Decide which values of X it includes, then pick the inequality, the scipy call and the Excel formula that add up exactly those values. The off-by-one trap and the sentences that count the other outcome are the point of the exercise.

Question 1

Right in this session: 0 of 0

A newsletter goes to 8 customers. Each opens it with probability 0.3, independently of the others.

Let X be the number of customers who open it.

What is the probability that the number of customers who open it is more than 2?

1. The inequality

P(X ≥ 4)

P(3 ≤ X ≤ 7)

P(X ≥ 3)

P(2 ≤ X ≤ 7)

2. In Python (scipy.stats)

binom.cdf(7, 8, 0.3) - binom.cdf(1, 8, 0.3)

binom.sf(1, 8, 0.3)

binom.sf(2, 8, 0.3)

binom.cdf(7, 8, 0.3) - binom.cdf(2, 8, 0.3)

3. In Excel

=1-BINOM.DIST(2, 8, 0.3, TRUE)

=1-BINOM.DIST(3, 8, 0.3, TRUE)

=BINOM.DIST(7, 8, 0.3, TRUE)-BINOM.DIST(1, 8, 0.3, TRUE)

=BINOM.DIST(7, 8, 0.3, TRUE)-BINOM.DIST(2, 8, 0.3, TRUE)

Words to probabilities