Based on a survey, assume that 27% of consumers are comfortable having drones

Question

Based on a survey, assume that 27% of consumers are comfortable having drones

Cheyanne Leigh 2021-09-15 Answered

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?

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Expert Answer

Alannej

Answered 2021-09-16 Author has 104 answers

Step 1
A binomial experiment is a discrete probability experiment which is repeated for a fixed number of trials, and each of the trial is independent of the other trial. The possible outcomes for each trail are two and they are defined as success (S) and failure (F).
Assume that the random variable X follows a binomial distribution with parameters n and p. So, the binomial probability is,

P (X = x) =^{n} C_{x} \times p^{x} \times q^{n - x}

Step 2
Here, x is the number of successes that results from the binomial experiment, n is the number of trials and p is the probability of success on an individual trial.
Step 3
The provided information are:
Number of trials

(n) = 4

Probability of success of each trial

(p) = 0.27

Probability of failure of each trial

(q) = 1 - 0.27 = 0.73

Number of successes

(x) = 2

Step 4
Consider, X be the random variable that represents the number of customers who are comfortable with delivery of their purchases by drones is binomially distributed.
The probability that exactly two of the customers are comfortable with delivery by drones can be computed as:

P (X = 2) =^{4} C_{2} \times {0.27}^{2} \times {0.73}^{42}

= 6 \times 0.0729 \times 0.5329

= 0.233

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