A survey finds customers are charged incorrectly for an item 20% of the time. Suppose a customer purchases 14 items. Find the probability that the customer is charged incorrectly on at least 3 items.

55.2% probability that the customer is charged incorrectly on at least 3 items.

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is charged incorrectly, or it is not. The probability of an item being charged incorrectly is independent from other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

A survey finds customers are charged incorrectly for an item 20% of the time.

This means that

Find the probability that the customer is charged incorrectly on at least 3 items.

Either the customer is charged incorrectly on 2 or less items, or he is charged on at least 3. The sum of the probabilities of these events is 1.

So

We want

So

In which

55.2% probability that the customer is charged incorrectly on at least 3 items.

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

40 minutes

step-by-step explanation:

add the time and multiply by 2