b This time we want to find the probability that a randomly chosen customer will have used the GPS system no more than 10 times. This is the same as finding the probability that the value of our random variable X is less than or equal to 10.
P(X≤10)= ?
Let's look at the table we made in Part A again.
Value of X
|
Customers
|
X=0
|
1382
|
1≤X≤5
|
2350
|
6≤X≤10
|
2010
|
11≤X≤15
|
1863
|
16≤X≤20
|
1925
|
X≥21
|
470
|
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 . Since the
3 events are , 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.
Value of X
|
Customers
|
Probability
|
Simplified
|
X=0
|
1382
|
100001382
|
0.1382
|
1≤X≤5
|
2350
|
100002350
|
0.235
|
6≤X≤10
|
2010
|
100002010
|
0.201
|
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%.