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#1, Exam Stat 215, Dr. M. Bohner. Feb 19, 2003. Instructions: Each problem is worth 20 points. Only responses entered in the allocated space (no extra space allowed) for each problem will be graded. Present only the complete solution including all explanation (without scratch work, use the back of the assignment sheet for that purpose) neatly. You must support all of your answers in order to receive credit. Do not remove the staples. Do not turn in the assignment sheet. Grades will be posted on the web tonight. 1. A bed and breakfast place has ten beds. During one year, the number of beds occupied per day is recorded. The result is: 3, 9, 30, 31, 39, 49, 47, 54, 52, 51 days for 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 beds, respectively. Find the sample mean, the sample median, the sample variance, and the empirical distribution function of the data. 2. The students who participated at the rst exams for statistics for and mathematics obtained the following grades (statistics in columns and mathematics in rows): A B C 6 D 0 4 F 0 0 2 A 25 12 C D B 11 33 15 0 0 20 45 27 5 21 58 21 F 0 0 12 26 57 Take the values 4 for A, 3 for B, 2 for C, 1 for D, and 0 for F to calculate the corresponding correlation coe cient. Explain. 3. Suppose P (A) = 0.75, P (B) = 0.25, and P (A \ B) = 0.5. Calculate P (A B), P (A B ), P (B \ A), P (A B ), and P (A B). 4. The same product is produced by four machines. The rst machine produces 15%, the second 20%, the third 25%, and the fourth 40% of the total production. The percentages of bad products of each machine are: 3%, 4%, 6%, 8%, respectively. Calculate the probability that a randomly selected product is bad. Also calculate the probability that a randomly selected product that turns out to be bad was produced by the rst (second, third, fourth) machine.

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