1. Media Matrix collected data showing the most popular websites when browsing at home and at work (Business 2.0, January 2000). Below are data showing the number of unique visitors (thousands) for the top 25 websites when browsing at home.

Website Unique visitors (thousands) Website Unique visitors (thousands)
about.com 5538 looksmart.com 5984
altavista.com 7391 lycos.com 9950
amazon.com 7986 microsoft.com 15593
angelfire.com 8917 msn.com 23505
aol.com 23863 netscape.com 14470
bluemountainarts.com 6786 *passport.com 11299
ebay.com 8296 real.com 6785
excite.com 10479 snap.com 5730
geocities.com 15321 tripod.com 7970
go.com 14330 xoom.com 5652
hotbot.com 5760 yahoo.com 26796
hotmail.com 11791 zdnet.com 5133
icq.com 5052

a. Compute the mean and median.

b. Do you think it would be better to use the mean or the median as the measure of central location for these data? Explain.

c. Compute the first and third quartiles.

2. Police records shows the following numbers of daily crime reports for a sample of days
during the winter months and a sample of days during the summer months.

Winter 18 20 15 16 21 20 12 16 19 20
Summer 28 18 24 32 18 29 23 38 28 18

a. Compute the range and interquartile range for each period

b. Compute the variance and standard deviation for each period

c. Compute the coefficient of variance for each period

d. Compare the variability of the two periods

3. Five observations taken for two variables follow.

Xi 4 6 11 3 16
Yi 50 50 40 60 30

a. Construct a scatter diagram with x on the horizontal axis.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Compute and interpret the sample covariance.

d. Compute and interpret the sample correlation coefficient.

4. PCWorld provided performance scores and ratings for 15 notebook PCs (PCWorld, February 2000). The performance score is a measure of how fast a PC can run a mix of common business applications as compared to a baseline machine. For example, a PC with a performance score of 200 is twice as fast as each notebook tested in the study, with higher scores indicating a better rating. The data are shown below

Notebook Performance score Overall rating
AMS Teach Roadster 15CTA380 115 67
Compaq Armada M700 191 78
Compaq Prosignia Notebook 150 153 79
Dell Inspiron 3700 C466GT 194 80
Dell Inspiron 7500 R500VT 236 84
Dell Latitude Cpi A366XT 184 76
Enpower ENP-313Pro 184 77
Gateway Solo 9300LS 216 92
HP Pavillion Notebook PC 185 83
IBM thinkPad I Series 1480 183 78
Micro Express NP7400 189 77
Micron TransPort NX PII-400 202 78
NEC Versa SX 192 78
Sceptre Soundx 5200 141 73
Sony VAIO PCG-F340 187 77

a. Construct a scatter diagram with performance score on the horizontal axis.

b. Is there any relationship between performance score and overall rating? Explain.

c. Compute and interpret the sample covariance.

d. Compute and interpret the sample correlation coefficient.

e. What does the sample correlation coefficient tell about the relationship between the performance score and the overall rating?

5. How many ways can three items be selected from a group of six items?

6. Consider the experiment of tossing a coin three times.

a. Develop a tree diagram for the experiment.

b. List the experimental outcomes.

c. What is the probability for each experimental outcome?

7. Military radar and missile detection system are designed to warn a country of an enemy attacks. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a 0.9 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions.

a. What is the probability that a single detection system will detect an attack?

b. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?

c. If three systems are installed, what is the probability that at least one of the systems will detect the attack?

d. Would you recommend that multiple detection systems be used? Explain.

8. The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of ten minutes. Answer the following questions.

a. What is the probability of completing the exam in one hour or less?

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes?

c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

9. Sales personnel for Skilling Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90 per cent and 95 per cent confidence intervals for the population mean number of weekly customer contacts for the sales personnel.