SOLUTION: Find the following binomial probabilities: a. n=8, p=.25, P(x = 4) b. n=16, p=.4, P(4≤ x ≤7) c. n=11, p=.5, P(x > 8)

Algebra ->  Probability-and-statistics -> SOLUTION: Find the following binomial probabilities: a. n=8, p=.25, P(x = 4) b. n=16, p=.4, P(4≤ x ≤7) c. n=11, p=.5, P(x > 8)      Log On


   

Question 600527: Find the following binomial probabilities:
a. n=8, p=.25, P(x = 4)
b. n=16, p=.4, P(4≤ x ≤7)
c. n=11, p=.5, P(x > 8)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

a)

P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 4) = (8 C 4)*(0.25)^(4)*(1-0.25)^(8-4)

P(X = 4) = (8 C 4)*(0.25)^(4)*(0.75)^(8-4)

P(X = 4) = (70)*(0.25)^(4)*(0.75)^4

P(X = 4) = (70)*(0.00390625)*(0.31640625)

P(X = 4) = 0.086517333984375


So the answer is P(X = 4) = 0.086517333984375


Note: n C x = (n!)/(x!(n-x)!)

So 8 C 4 = (8!)/(4!(8-4)!) = 70