MGMT2262

Worksheet #3

1) Suppose a distribution has a mean of 24 and standard deviation of 3.2. Between which 2 values would at least 8/9 of the distribution fall? (14.4 and 33.6)

2) For the distribution in question 1, how many standard deviations from the mean are 19.008 and 28.992? (1.56)

3) Sometimes Chebyshev’s theorem is used for samples. For this data set:

2.8	3.8	4.3	4.6	4.8	4.9	5.2	5.3	5.9	7.1
2.9	3.9	4.5	4.6	4.8	4.9	5.2	5.7	6.2	7.3
3.2	4.1	4.5	4.7	4.9	5.1	5.3	5.8	6.4	7.8

confirm Chebyshev’s theorem for k=2. (The actual percentage is 96.67%)

4) Suppose the number of videos that people rent in a month follows the following distribution:

Number of videos	Percentage
0	0.2
1	0.28
2	0.37
3	0.15

Verify that this is a proper probability distribution (see key)

5) Compute the mean and standard deviation of the number of videos people rent in a month. Confirm Chebyshev’s theorem for k=2. (m = 1.47; s = 0.9742; 100% of the distribution lies with 2 standard deviations of the mean)

6) Suppose it costs a video store $15 to buy a movie wholesale. Here is the distribution of the number of times a video is rented:

Frequency	Percentage
0	0.02
10	0.22
20	0.34
30	0.24
40	0.12
50	0.06

If the store wants to realize an average profit of at least $80 per video, what should be the minimum amount it should charge to rent it? Round to the nearest nickel. ($4.00)

7) Suppose that a certain auto manufacturer has 24 models in its lineup and that 9 of these vehicles require less than 8 L per 100 km in the city. If 6 of the models are randomly selected, what is the probability that no more than 2 of them require less than 8 L per 100 km in the city? (60.31%)

8) Suppose that 9 of the models are randomly selected. What is the probability that at least 7 of them require at least 8 L per 100 km in the city? (22.53%)

9) Sam is an office supplies salesperson. On average, he gets a sale 20% of the time after meeting with the prospect. If he meets with 4 prospects in a week, what is the probability he will get exactly 1 sale? (40.96%)

10) If he meets with 10 prospects, what is the probability he will get fewer than 2 sales? (37.59%)

11) If he meets with 25 prospects in a month, what is the probability he gets at least 2 sales? (97.26%)

12) In a year, he usually meets with 300 prospects. If his average commission is $2500, what is his average commission in a year? What is the maximum commission he can expect 99.7% of the time, rounding to the nearest thousand? (mean = $150,000; maximum = $202,000)

13) Suppose programmers at a software company average 1 bug for every 10,000 lines of code. What is the probability a program with 10,000 lines of code will be bug free? (36.79%)

14) What is the probability a program with 25,000 lines of code will have at least 2 bugs? (71.27%)

15) What is the probability a program with 5,000 lines of code will have at least 1 bug but no more than 3? (39.17%)

16) Suppose a program has 3.5 million lines of code. What would be the mean and standard deviation of the number of bugs in the program? (mean = 350; standard deviation = 18.7083)

17) Suppose a pizza delivery driver can deliver 4 pizzas per hour on average. What is the probability a driver can deliver no more than 3 pizzas in an hour? (43.35%)

18) What is the probability a driver can deliver at least 5 pizzas in an hour? (37.12%)

19) Suppose the pizza restaurant has 2 drivers. What is the probability the 2 drivers can deliver at least 10 pizzas in an hour? (28.34%)

20) According to Chebyshev’s theorem, m + 3s represents a reasonable upper limit on a distribution. If the 2 drivers both work an 8-hour shift, what is the maximum number of pizzas the restaurant can expect them to deliver? (88)