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stats practice midterm 2 solutions

# stats practice midterm 2 solutions - STUDENT ID Midterm...

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STUDENT ID #: Midterm Exam MATH 203 Principles of Statistics I October 22, 2003 Student Name: Notes: You can use the back of the page if your answers do not fit in the spaces provided (but if your answer doesn't fit, it probably is too long). Explanations for questions 1 and 2 should be very short and do not require full sentences. You do not have to reduce fractions (especially if you do not have a calculator). No points will be taken off for arithmetic errors as long as all work is shown. Please make sure your student ID # is on all pages.

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STUDENT ID #: Question 1 (10 points): Let the probabilities of the sample points for the Venn Diagram above be the following: Pr(1) = 0.0 Pr(2) = 0.3 Pr(3) = 0.1 Pr(4) = 0.3 Pr(5) = 0.2 Pr(6) = 0.1 (a) 5 points What is Pr(A|B)? Are A and B independent? Pr(A|B) = Pr( A int B)/Pr(B) = Pr( 2 ) / Pr( 2 or 3 or 4) = .3/.7 = 3/7 (3 pts) Pr(A) = Pr(1 or 2) = 0 + 0.3 = 0.3 which is not equal to 3/7, so A and B are not independent. (2 pts) (b) 5 points What is Pr(A c U B c )? Are A and B mutually exclusive? Pr(A c U B c ) = Pr( (A int B) c ) = 1 - Pr(A int B) = 1- .3 = 0.7 (3 pts) Pr( A int B) = 0.3, so A and B are not mutually exclusive.
STUDENT ID #: Question 2 (10 points): (a) 5 points Using the histogram above and what you have learned in class, “guess” the order for the mean, median, and mode. List the three terms in order from SMALLEST TO LARGEST. Mode < median < mean (b) 5 points The mean of the sample shown above is 10. The standard deviation is also 10. Give an interval that is guaranteed to contain at least 68% of the sample data . Hint: Things in bold are usually important and possibly trickery. Using Chebyshev's, we know that an interval of (-10, 30) will contain at least 75% of the observations, which means that it will also contain at least 68% of the data. You can't use the empirical rule, because the data are not symmetric. myexps Rel. Frequency 0 20 40 60 80 0.00 0.02 0.04 0.06

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STUDENT ID #: Question 3 (15 points): The type of medical care a patient receives may vary with the age of the patient. A large study of women who had lumps on their breasts investigated whether or not each woman
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stats practice midterm 2 solutions - STUDENT ID Midterm...

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