Question

Find the expected value, μ, and standard deviation, σ, for a binomial random variable with each of the following values of n and p. (Round all answers for σ to four decimal places.)

(a) n = 40, p = 1/2.

μ =

σ =

(b) n = 100, p = 1/4.

μ =

σ =

(c) n = 2500, p = 1/5.

μ =

σ =

(d) n = 1, p = 0.1.

μ =

σ =

(e) n = 30, p = 3/10.

μ =

σ =

Answer 1

Solution :

Given that,

Using binomial distribution,

(a)

Mean = = n * p = 40 * 0.5 = 20

Standard deviation = = n * p * q = 40 * 0.5 * 0.5 = 3.1623

(b)

= 25

= 4.3301

(c)

= 500

= 20

(d)

= 0.1

= 0.3

(e)

= 9

= 2.5100