a game superstore manager made claims that the probability that a customer would prefer the deluxe model to the standard model of a product is 30%.
what is the probability that more than three out of 10 customers will prefer the standard model
We can approach this problem by using the binomial distribution formula, which gives us the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success. In this case, the number of trials is 10 (since there are 10 customers), the probability of success (i.e., a customer preferring the standard model) is 70% (since 30% prefer the deluxe model), and we want to know the probability of getting more than three successes.
Using a binomial probability calculator or software, we can find that the probability of getting exactly three successes is approximately 0.266, and the probability of getting fewer than three successes is approximately 0.040. Therefore, the probability of getting more than three successes is:
P(X > 3) = 1 - P(X ≤ 3)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
= 1 - 0.040
= 0.96
So the probability that more than three out of 10 customers will prefer the standard model is approximately 0.96 or 96%.