Making Predictions with Experimental Probability Warm Up Probabilities

Making Predictions with Experimental Probability

Warm Up

• Probabilities can be used to make predictions in daily life. • A prediction is something that can reasonably be expected to happen in the future. • A qualitative prediction can help formulate decisions about which situation is more likely. • Proportional reasoning can be used to make quantitative predictions and to compare options in real-world situations. • To make predictions using experimental probability first, write an equation to find the likelihood of the event. Use the likelihood to make the prediction.

A hotel keeps records of its room reservations. The hotel’s manager notices that, on average, 4% of reservations are cancelled per month. He predicts that 15 reservations will be cancelled out of the 250 total reservations during next month. Is his prediction reasonable? Explain. How could you solve this problem using a proportion?

Roll a number cube 20 times, recording multiples of 3 rolled. How can you use the experimental probability of a success to predict the number of successes in 100 rolls?

Lorenzo found that his experimental probability of getting a hit is 40%. Out of 350 at bats, about how many hits could he predict he would make?

The owner of a rafting company notices that 16% of customers call to cancel before a guided rafting trip. The owner predicts that of 850 customers booked for the week, 102 will cancel. Do you agree with the prediction? Explain.

How can you use experimental probability to make qualitative and quantitative predictions and use the predictions to draw conclusions? Solve a proportion or an equation that uses the experimental probability to make a prediction. Then compare the prediction to additional data to draw a conclusion.

On average, a gym claims that 85% of its members renew their memberships every year. If the gym has 400 members, predict how many will renew their membership. Is the gym’s claim accurate if 330 members renew their memberships?

A hotel manager finds that on average 86% of customers keep their reservations each week. The manager predicts that out of 2, 200 reservations next week, 300 customers will cancel. He thinks they should overbook the hotel by 42 reservations each day. Do you agree with the manager? Explain.

A gas pump machine rejects 12% of credit card transactions. If this is twice the normal rejection rate for a normal gas pump, how many out of 500 credit cards transactions would a normal gas pump machine reject?

Exit Ticket 1. A librarian noticed that 60% of seventh graders checked out fantasy books. About how many of 240 seventh graders would check out fantasy books? 2. A tennis player gets an ace on 35% of his serves. Out of 80 serves, about how many aces will he get? 3. A light bulb manufacturer finds that 4% of the bulbs it makes are defective. The quality control officer predicts that 700 bulbs will be defective out of 15, 500 bulbs made. Do you agree? Explain. 4. A delivery service claims that orders arrive before noon 90% of the time. If Amy uses the delivery service 20 times, how many times can she predict the deliveries will arrive before noon? Is the claim accurate if her packages arrive after noon 4 times?