Question

based on a survey, assume that 27% of consumers are comfortable having drones deliver their purchases. suppose that we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with delivery by drones. identify the values of n, x, p, and q.
the value of n is 4.
(type an integer or a decimal. do not round.)
the value of x is □.
(type an integer or a decimal. do not round.)

Explanation:

Step1: Identify the binomial probability formula parameters

In the binomial probability formula \(P(X = x)=C(n,x)\times p^{x}\times q^{n - x}\), \(n\) is the number of trials, \(x\) is the number of successes, \(p\) is the probability of success on a single - trial, and \(q = 1 - p\) is the probability of failure on a single - trial.
We are given that \(n = 4\) (since we are considering 4 consumers). The number of successes \(x=2\) (exactly 2 consumers are comfortable). The probability of success \(p = 0.27\) (27% of consumers are comfortable). Then \(q=1 - p=1 - 0.27 = 0.73\).

Answer:

\(n = 4\), \(x = 2\), \(p = 0.27\), \(q = 0.73\)