11. Binomial Distribution

Question 1

For a sample of 10 students, X, the number of students who have tried marijuana, has the Binomial(10, 0.3) distribution. For "at least half" we want P(X ≥ 5). From Table 11.4 this is 0.150, or 15%.

With a sample of 20 students we want P(X ≥ 10) where X now has the Binomial(20, 0.3) distribution. Table 11.4 shows this is 0.048, or 4.8%. So the chance of getting "at least half" is smaller with the larger sample size.

Question 2

There is a discrepancy between the tables for the Binomial(3, .25) distribution. In Table 11.3 we find P(X = 2) = .141 and P(X = 3) = .016, so P(X ≥ 2) = .141 + .016 = .157.

In contrast, Table 11.4 gives P(X ≥ 2) = .156. This is the correct value. The value from Table 11.3 involves two rounding errors and so is not as accurate.