If n=7 and p= 0.3, find P (x=4). Round your answer to four decimal places.
To find P(x=4) when n=7 and p=0.3, we will use the binomial probability formula:
P(x=k) = (n choose k) * p^k * (1-p)^(n-k)
First, we need to calculate (7 choose 4), which is equal to 7! / (4!(7-4)!).
(7 choose 4) = 7! / (4!(7-4)!) = 7! / (4! * 3!) = (7*6*5) / (3*2*1) = 35
Next, we plug the values into the formula:
P(x=4) = (7 choose 4) * (0.3)^4 * (1-0.3)^(7-4)
P(x=4) = 35 * (0.3)^4 * (0.7)^3
P(x=4) = 35 * 0.3^4 * 0.7^3
P(x=4) = 35 * 0.0081 * 0.343
P(x=4) = 0.0950115
Therefore, P(x=4) when n=7 and p=0.3 is approximately 0.0950 when rounded to four decimal places.