Question

For a binomial process, the probability of success is 40 percent and the number of trials is 5.

a. Find P(X > 4) (round to four decimal places).

b. Find P(X ≤ 1) (round to four decimal places).

c. Find the standard deviation (round to three decimal places).

Answer 1

Solution

Given that ,

p = 0.40

1 - p = 0.60

n = 5

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

a)

P(X > 4) = P(X = 5)

P(X = ) = ((5! / 5! (5 - 5)!) * 0.40⁵ * (0.60)^{5 - 5}

Probability = 0.0102

b)

P(X 1) = P(X = 0) + P(X = 1)

= ((5! / 0! (5 - 0)!) * 0.40⁰ * (0.60)^{5 - 0} + ((5! / 1! (5 - 1)!) * 0.40¹ * (0.60)^{5 - 1}

= 0.0778 + 0.2592

Probability = 0.3370

c)

Standard deviation = n * p * ( 1 - p ) = 5 * 0.40 * 0.60 = 1.095