Question

Given a binomial distribution, n = 7 and π= .30. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.)

A) x = 2

B) x = 3

Answer 1

Solution

Given that ,

= 0.30

1 - = 0.70

n = 7

A) x = 2

Using binomial probability formula ,

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

P(X = 2) = ((7! /2 ! (7-2)!) * 0.30² * (0.70)^7-2

=  ((7! / 2! (5)!) * 0.30³ * (0.70)⁵

= 0.3177

Probability = 0.3177

B) x = 3

Using binomial probability formula ,

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

P(X = 2) = ((7! /3 ! (7-3)!) * 0.30³ * (0.70)^7-3

=  ((7! / 3! (4)!) * 0.30³ * (0.70)⁴

= 0.2269

Probability = 0.2269