Question

A binomial experiment for the random variable X was performed with 10 trials. The probability of success was found to be 0.17. Determine the following probabilities: a.) P(X = 3)= b.) P(X < 3) = c.) P(X > 7) =

Answer 1

The probability of p(x = 3) , p(x < 3) and p(x > 7) are 0.160, 0.7659 and 0.0003 respectively.

Using the binomial probability formula ;

• 
  `nCx * p^(x) * (1-p)^(n-x)`
• n = 10
• p = 0.17

1.)

P(X = 3) =
`10C3 * 0.17^(3) * (1-0.17)^(7) = 0.160`

2.)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1552 + 0.3178 + 0.2930

P(X < 3) = 0.7659

3.)

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)

P(X > 7) = 0.0003