Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥16), n=19, p=0.7

Answer 1

Solution:

Given that,

P = 0.7

1 - P = 0.3

n = 19

Here, BIN ( n , P ) that is , BIN (19 , 0.7)

then,

n*p = 13.3 > 5

n(1- P) = 5.7 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 13.3

Standard deviation = =n*p*(1-p) = 3.99

We using continuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 15.5) = 1 - P(x < 15.5)

= 1 - P((x - ) / < (15.5 - 13.3) /3.99 )

= 1 - P(z < 1.10)

= 1 - 0.8643

= 0.1357

Probability = 0.1357