STAT177 Assignment #2

Due February 11, 2008

Note: Express all probabilities as decimals accurate to 4 decimals (0.1234) or as percentages accurate to 2 decimals (12.34%) unless otherwise stated. Each question is worth 1 mark.

For a particular auto service club, a tow truck can service 2.4 vehicles per hour on average.

1) If there are 6 trucks working, what is the probability they can collectively service at least 12 vehicles in an hour?

2) If there are 6 trucks working, what is the probability they can collectively service no more than 50 vehicles in a 4-hour period?

3) If there are 8 trucks working, what is the most number of vehicles they can be expected to service in a 6-hour period based on m + 3s? Round to the nearest whole number.

For a customer waiting for service from this club, the average wait time is 24 minutes when there are 6 trucks working.

4) If there are 6 trucks working, what is the probability someone will wait more than 30 minutes?

5) If there are 8 trucks working, what is the probability someone will wait less than 15 minutes?

6) If there are only 2 trucks working, what is the probability someone will wait more than 90 minutes in total if the person has been waiting 40 minutes already?

For the auto service club, the amount it spends on gasoline per week for its fleet of tow trucks is normally distributed with a mean of $960 and standard deviation of $152.

7) In a given week, what is the probability it spends more than $1000 on gasoline?

8) In a given week, what is the probability it spends less than $750?

9) What is the most the club should have to budget per week for gasoline 99% of the time? Round to the nearest dollar.

10) For a sample of 6 weeks, what is the probability the total amount the club spends on gasoline during this period is more than $5700?

Suppose the auto service club invests in refitting its trucks to propane in an effort to significantly reduce its average weekly expenditure of $960.

11) State the null and alternative hypotheses.

12) Suppose the p-value from the analysis is 12.4%. If the hypothesis were tested at a 5% level of significance, what conclusion should be reached?

13) Suppose a level of significance had not been chosen. Why would the same conclusion be reached?

Suppose that on any given winter night, 72% of vehicles are plugged in.

14) For a sample of 24 vehicles, what is the probability that at least three-quarters of them are plugged in?

15) For a sample of 50 vehicles, what is the probability that no more than 10 of them are not plugged in?

16) For a sample of 10,000 vehicles, what is the most number that can be expected to be plugged in 99.7% of the time?