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 formula for binomial cumulative distribution is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), and \(P(X\lt4)=P(X = 0)+P(X = 1)+P(X = 2)+P(X = 3)\)
Using technology (such as a TI - 84 Plus: press 2nd VARS (DISTR), then binomcdf). Enter binomcdf(n = 8,p = 0.65,x = 3)

Step2: Calculate the value

When we calculate binomcdf(8,0.65,3) on a calculator, we get the result.

Answer:

\(0.1052\)