Question

65 percent of consumers prefer to purchase electronics online. You randomly select consumers. Find the probability that the number of consumers who prefer to purchase electronics online is​ (a) exactly​ five, (b) more than​ five, and​ (c) at most five.

Answer 1

Step-by-step explanation:

To calculate the probabilities, we can use the binomial probability formula. In this case, we have a binomial distribution with the following parameters:

Probability of success (p): 65% or 0.65

Number of trials (n): The number of consumers randomly selected

Number of successes (k): The number of consumers who prefer to purchase electronics online

(a) To find the probability that exactly five consumers prefer to purchase electronics online, we can use the formula:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

Plugging in the values, we get:

P(X = 5) = (nC5) * 0.65^5 * (1 - 0.65)^(n - 5)

(b) To find the probability of more than five consumers preferring to purchase electronics online, we need to calculate the cumulative probability from k = 6 to the maximum number of consumers randomly selected. This can be calculated as follows:

P(X > 5) = 1 - P(X <= 5)

(c) To find the probability of at most five consumers preferring to purchase electronics online, we need to calculate the cumulative probability from k = 0 to k = 5. This can be calculated as follows:

P(X <= 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)