Exercise 1 Page 806

Since X represents the number of uses of a GPS, we can rewrite the first column using our random variable X.

To find P(X>20) we need to find the number of customers that have used the GPS system more than 20 times. Looking at the table we can tell that there is only one outcome where X>20. To find the probability, we will use the Probability Formula. P(X>20)=Customers for whom X>20/Customers surveyed We are given that the car dealership surveyed 10 000 of its customers with a GPS and we have found that the number of customers for whom X>20 is 470. P(X>20)=470/10 000=0.047 The probability that a randomly chosen customer will have used the GPS system more than 20 times is equal to 0.047, which can also be written as 4.7 %.

We will consider the first 3 rows of our table only because the value of X is less than or equal to 10 in these rows. Our event is made up of 3 more simple events, so this is a compound event. Since the 3 events are mutually exclusive events, we can calculate P(X ≤ 10) by adding the probabilities that each event occurs. P(X ≤ 10) &= P(X = 0) + P(1≤ X ≤ 5)& + P(6 ≤ X ≤ 10) We will calculate each probability using the Probability Formula. Probability of each event is equal to the number of customers that are related to the given event divided by the total number of customers which is 10000.

Now we can substitute in the values from the table into our equation for P(X≤ 10). P(X≤ 10) &= 0.1382 + 0.235+0.201 &= 0.5742 ≈ 0.574 The probability that a randomly chosen customer will have used the GPS system no more than 10 times is equal to 0.574, which can also be written as 57.4 %.