Question

a binomial probability experiment is conducted with the given parameters. use technology to find the probability of x successes in the n independent trials of the experiment.
n = 8, p = 0.65, x < 4
p(x < 4) =
(round to four decimal places as needed.)

Explanation:

Step1: Use binomial cumulative distribution function

The binomial cumulative distribution function is \(P(X = k)=\binom{n}{k}p^{k}(1 - p)^{n - k}\), and \(P(X\lt4)=P(X = 0)+P(X = 1)+P(X = 2)+P(X = 3)\)

Using a calculator or software (such as TI - 84: binomcdf(n,p,x) where \(n = 8\), \(p=0.65\), \(x = 3\))

Step2: Calculate the probability

When using technology (e.g., in R: pbinom(3,8,0.65)), we get the result.

Answer:

\(0.1061\)