EXAMPLE 2 Eric always arrives at his bus stop at 10:05 am, knowing that the arri
ID: 3064526 • Letter: E
Question
EXAMPLE 2 Eric always arrives at his bus stop at 10:05 am, knowing that the arrival of the bus varies waits for the bus to arrive. 1. What is the probability that Eric will have to wait longer than 8 minutes? What anywhere from 10:05 am to 10:20 am. Let X be the amount of time (in minutes) that Eric distribution and parameters are you using? 2. What is the probability the bus will come between 10:12 am and 10:18 am? 3. Eric has been keeping a record of his wait times for the bus, what is the 40th percentile of his wait times? What time is that on the clock? minutes His class begins at 10:30 am. What is the probability that he will be on time for class? 4. If Eric's waiting time is at most 9 minutes, what is the probability that it is under 6 5. After Eric gets on the bus, he has a 10 minute ride and then a 4 minute walk to his classExplanation / Answer
As the probability is normally distributed the wait time ranges from (0,15) minutes with equal probability 1/15, thus
1. P(x>=8)=7/15, Distribution is uniform and parameters are (0,15)
2. Between 10:12 and 10:18, P=6/15=2/5
3. 40 th percentile of wait times is 0.4*15=6 minues wait time, thus the time would e 10:11
4. If wait time is atmost 9 minutes then P(x<=6|x<=9)=6/9=2/3
5. The class begins at 10:30, going back from here 4 minutes it takes to walk, thus bust has to reach latest by 10:26, the ride takes 10 minutes, thus Eric has to board the bus before 10:16, Thus P=(16-5)/15=11/15
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