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# Public Safety and Speeding Tickets: Probabilities

The department of public safety surveyed drivers to see how many of them had received a speeding ticket for driving at least 20 MPH above the posted speed limit. It was reported that 25% of the licensed drivers in a certain county had received speeding tickets for driving 20 MPH above the posted speed limit. In June, 30 licensed drivers will be randomly surveyed.

What is the probability that 15 of the 30 drivers will have received a speeding ticket for driving 20 MPH over the posted speed limit?

What is the probability that at least 13 of those 30 drivers will have received a ticket for driving at least 20 MPH over the posted speed limit?

What is the probability that 10 or less of the 30 drivers will have received a ticket for driving at least 20 MPH over the posted speed limit?

What type of probability function should be used to analyze this study?

What is the mean and standard deviation of this? What is the formula and the value?

#### Solution Preview

Suppose X is the number of drivers who will receive a speeding tickets. Then X satisfies the Binomial distribution B(30, 0.25). We can also use the normal distribution to approximate B(30, ...

#### Solution Summary

This solution calculates the probabilities that drivers will receive a speeding ticket. It also looks at the probability function used, the mean, and standard deviation.

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