- You are analyzing the performance of three sales areas. Box plots of the number of sales each day for these three different areas are given below: The "whiskers" are drawn with solid lines. 10 15 20 H 25 4 Sales Area 1 30 Sales Area 3 Sales Area 2 45 35 40 4 (a) Which sales area had the best single day's sales, and how many sales were there? (b) Which sales area had the worst single day's sales, and how many sales were there? (c) What does the* (the asterisk) for the plot for Sales Area 1 mean? (d) For Area 2, how many sales were there on the second worst day and on the second best day? (e) For Sales Area 1 and Sale Area 2, look at the 'box' of each boxplot to determine if the shape is skewed right, skewed left or symmetrical about the mean? Why? rom marks for an FMGT set with 22 students (in order): 50 Below are the actual Business Math final exam marks for an FMGT set with 22 students (in order) 13 29.5 36 44 45 55 70 61 62.5 64.5 69 77.5 79 80 83 84.5 87 96 96 73 74 76.5 (a) Calculate the first quartile, median and third quartile. (b) Looking at the quartiles and median, is the distribution of marks skewed left, skewed right, or symmetrical about the mean? Explain. (Hint: sketch the 'box' of the boxplot). (c) Calculate the IQR (d) Is the final exam mark of 13 an outlier? Why or why not? (e) Where would the whisker on a boxplot of the marks extend to on the low side? Annual sales, in millions of dollars, for 21 pharmaceutical companies are below: 600 739 4341 5794 1356 1374 1825 1875 2127 2459 2818 3653 4000 6452 7478 8300 8400 8879 10498 11413 14000 (a) (i) Do a 5-number summary. (ii) The middle 50% of sales are between what two values? (b) Calculate the interquartile range and the lower and upper limits. (c) Are there any outliers? (d) Johnson's & Johnson's sales are the highest at $14,000 million. Suppose a data entry error (transposition error) has been made and the sales had been entered as $41,000 million. Would you have caught this problem by looking at the upper limit? OPMT 1197 Business Statistics Germain Tanoh Summer 2021 (e) For a boxplot of the sales, where would the box extend to? Where would the whiskers end? Describe the shape of the distribution. www 611 @ McMansion Realty is a real estate firm that sells high-end properties and estates located throug the United States. The prices listed (in $1,000's) for 22 properties are shown below: 999 1019 1025 1099 1119 1150 1170 1199 1280 1295 1300 1500 1650 1680 1795 1900 2150 2600 2895 3395 3500 4900 (a) (i) Do a 5-number summary (ii) The middle 50% of prices are between what two values? (b) Calculate the interquartile range and the lower and upper limits. (c) The highest priced property, $4,900,000, is listed as an estate overlooking White Rock Lak Dallas, Texas. Should this property be considered an outlier? Should the second highest p property listed for $3,500,000 be considered an outlier? Explain. (d) Do a boxplot (e) Describe the shape of the distribution. P(A) = probability that event A occurs = Lab Exercises 1. The manager of a Marvin Gardens, a large apartment complex, provides the following probabilities to estimate the number of vacancies that will exist next month: A Vacancies 0 1 2 3 4 5 Number of ways that A can occur Total number of possible outcomes Probability 0.05 0.15 0.35 0.25 0.10. 0.10 A: Are these valid probability assignments? B: Find the probability there are (a) no vacancies? (b) at least 4 vacancies? (c) at most 2? 2. If the probabilities are 0.05, 0.14, 0.17, 0.33, 0.20 and 0.11 that consumers will rate a new product: very poor, poor, fair, good, very good, or excellent, respectively, what are the probabilities that a consumer selected at random will rate the new product: (a) very poor or poor? (b) good, very good, or excellent? (c) good, given that you know that the rating is in the group (good, very good or excellent)? 3. If F and T are the events that a one-car driver in a certain age bracket will drive a Ford or a Toyota, and P(F) = 0.34 and P(T) = 0.08, find the probabilities that such a person will: (a) not drive a Ford (b) drive either a Ford or a Toyota (c) drive neither a Ford nor a Toyota. 4. An article in Cat Lover's Monthly asked 40 randomly selected cat owners to rank their cat's behavior from rotten to excellent. The results are summarized in the table below: Rating Excellent Number of Owners 2 3 5 6 24 40 What percentage of owners rated the cat's behaviour as (a) excellent? (b) at least good? (c) rotten? Very Good Good Mediocre Rotten Total 5. A batch of 50 parts contains 6 defective parts. (a) If the two parts are randomly selected one at a time without replacement, what is the probability that both parts are defective? OPMT 1197 Business Statistics Germain Tanoh Summer 2021 (b) If, instead, the first part is put back into the batch and then the second part is selected (sampling with replacement) what is the probability that both parts are defective? 6. Brendan recently graduated from the BCIT Marketing program. He hasn't found a job yet so he spends a lot of time working out at the gym and taking Zumba dance classes. He now looks buff so he decides to apply for a job working as a male dancer at two downtown clubs; the Foxy Lady and Thunder from Down Under. He estimates the probability he will get a job offer from Foxy Lady is 0.40, and from Thunder from Down Under it is 0.30. Assuming that the two job offers are independent of each other, what is the probability that (a) both clubs offer him a job? (b) he gets at least one offer? (c) he gets no job offer? 7. Suppose that P(A) = 0.30, P(B) = 0.50 (a) Find the probability of A or B if A and B are: (i) mutually exclusive (ii) independent (b) Find P(BA), if A and B are independent. 8. Reality TV has a new reality TV series called "Who Wants To Marry a Bigamist". In the exciting final episode the bigamist will ask two contestants to marry him. The executives have determined that there is a 40% chance that Agnes will say yes and a 50% chance Bertha will say yes. Agnes will be asked first and if she says yes the probability that Bertha will say yes will drop to 20%. What is the probability at least one of the women will say yes? 9. A quiz contains two questions. 90% of students get the first question correct, 5% get neither question correct, and 50% get both questions correct. Set up a 2x2 probability table and find the probability that a randomly selected student (a) Gets only the first question correct. (b) Gets at least one of the questions correct. (c) Gets either the 1st or 2nd question correct but not both (ie. gets only one question correct). 50.30.G)055