Determine the mean and standard deviation of the variable X in each of the following binomial...

Question

Question

Determine the mean and standard deviation of the variable X in each of the following binomial distributions. a. n= 3 and 1 =

Answer 1

Answer #1

Solution :

Given that,

Using binomial distribution,

(a)

Mean = $\mu$ = n * $\pi$ = 3 * 070 = 2.1

Standard deviation = $\sigma$ = $\sqrt$ n * $\pi$ * (1- $\pi$ ) = $\sqrt$ 3 * 0.70 * 0.30 = 0.7937

(b)

Mean = $\mu$ = n * $\pi$ = 3 * 0.80 = 2.4

Standard deviation = $\sigma$ = $\sqrt$ n * $\pi$ * (1- $\pi$ ) = $\sqrt$ 3 * 0.80 * 0.20 = 0.6928

(c)

Mean = $\mu$ = n * $\pi$ = 4 * 0.40 = 1.6

Standard deviation = $\sigma$ = $\sqrt$ n * $\pi$ * (1- $\pi$ ) = $\sqrt$ 4 * 0.40 * 0.60 = 0.9798

(d)

Mean = $\mu$ = n * $\pi$ = 4 * 0.70 = 2.8

Standard deviation = $\sigma$ = $\sqrt$ n * $\pi$ * (1- $\pi$ ) = $\sqrt$ 4 * 0.70 * 0.30 = 0.9165

Answer 2

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