Answer:
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)