Question

If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = ______.

Options

• 0.4

• 0.8

• 0.18

• 0.2

Answer 1

If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = 0.2.

Explanation:

In Binomial distribution,

Mean (µ) = np

and variance (σ²) = npq

Given, µ + σ² = 1.8

np + npq = 1.8

np + np(1 - p) = 1.8

5p + 5p - 5p² = 1.8   ...[∵ n = 5]

5p² - 10p + 1.8 = 0

5p² - 9p - p + 1.8 = 0

⇒ 5p(p - 1.8) - 1(p - 1.8) = 0

⇒ (5p - 1)(p - 1.8) = 0

⇒ p = 0.2  (p ≠ 1.8)   (∵ p ≤ 1)