Question

Use the binomial distribution: If n9 and p = 0.5, find P(x4) P(x = 4) = (Round your answer to 4 places after the decimal point, if necessary.)

Answer 1

To find P(x=4) using the binomial distribution, we can use the formula:

P(x=k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, k is the number of successes, p is the probability of success in each trial, and (n choose k) is the binomial coefficient.

In this case, n = 9, p = 0.5, and we want to find P(x=4).

Using the formula, we have:

P(x=4) = (9 choose 4) * (0.5)^4 * (1-0.5)^(9-4)

Calculating this value:

P(x=4) = (9! / (4! * (9-4)!)) * (0.5)^4 * (0.5)^5
= (126 / (24 * 5)) * 0.0625 * 0.03125
= 0.1641 (rounded to 4 decimal places)

So, P(x=4) = 0.1641.