(3 points) In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arrested previously for a DUI offence. Suppose 28 people arrested for DUI in Illinois are selected at random. You may assume that this is a binomial distribution. (0.5 pts.) a) What is the probability that exactly 3 people are repeat offenders

22.60% probability that exactly 3 people are repeat offenders

Step-by-step explanation:

For each driver arrested selected, there are only two possible outcomes. Either they are repeat offenders, or they are not. The probability of an arrested driver being a repeat offender is independent from other arrested drivers. So we use the binomial probability distribution to solve this problem.

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.

In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders;

This means that

Suppose 28 people arrested for DUI in Illinois are selected at random.

This means that

a) What is the probability that exactly 3 people are repeat offenders

This is

22.60% probability that exactly 3 people are repeat offenders

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.

answer:      

step-by-step explanation: