MA 180/418 Midterm Test 1, Version B Fall 2011

Transcription

1 MA 80/48 Midterm Test, Version B Fall 20 Student Name (PRINT): Student Signature: The test consists of 0 questions. Questions through 5 are multiple-choice and worth 5 points each. Questions 6 through 0 are computational and worth 5 points each. For questions through 5, circle the correct answer (a, b, c, or d) after each question. Each question is 5 points. No partial credit. Q What is the meaning of the term probability distribution? (a) A probability distribution is a statement of all possible outcomes of a procedure, probabilities is.0. (b) A probability distribution is a statement of all possible outcomes of a procedure, probabilities is between 0.0 and.0. (c) A probability distribution is a statement of all possible outcomes of a procedure, probabilities is 0.0. (d) A probability distribution is a statement of all possible outcomes of a procedure, probabilities is at least.0. Q2 Which statement about independent events is correct? (a) Independent events cannot occur simultaneously. (b) Given an event A, the complementary event Ā is independent of A. (c) Independent events divide the sample space into non-overlapping parts. (d) Independent events do not affect probabilities of one another.

2 Q5 Which formula is correct for the standard deviation of a population? (a) The standard deviation is s = n (x x)2. (b) The standard deviation is s = n (x x)2. (c) The standard deviation is σ = N (x µ)2. (d) The standard deviation is σ = N (x µ)2. Q4 What are usual z-scores? (a) Usual z-scores are those whose probability is greater than 5%. (b) Usual z-scores are 2 and 2. (c) Usual z-scores are those between 2 and 2. (d) Usual z-scores are those between 3 and 3. Q5 Which statement regarding usual and unusual values for a probability distribution is correct? (a) If a value is less than the maximum usual value, then it is usual. (b) If a value is greater than the minimum usual value, then it is usual. (c) The usual values are those whose probability is greater than 5%. (d) The usual values are within two standard deviations from the mean. 2

3 For questions 6 through 0, write your answer in the space provided. Show your work. Each question is worth 5 points. Q6 Listed below are the numbers of bankruptcy filings in Dutchess County, New York State, for each month in a certain year: Find the following measures for this sample (round off to one decimal place): Range = Midrange = Mean = Median = St. Deviation = Variance = Use the range rule of thumb to find: Minimum usual value = Maximum usual value = [Bonus] Find all quartiles and give the five-number summary: Q7 Assume that a procedure yields a binomial distribution with a trial repeated 4 times, and the probability of success on each trial is Round off your answers to four decimal places. (a) Find the probability that exactly 3 successes are observed: P (3) = (b) Find the probability that at most 3 successes are observed: P (at most 3) = [Bonus] Which question, (a) or (b), is relevant for determining whether 3 is an unusually low number of successes? [Bonus] Is 3 an unusually low number of successes? Why or why not? 3

4 Q8 Assume that 5% of all donors have type A blood. A sample of 80 donors is randomly selected. (a) Check the conditions under which the Normal Approximation to Binomial can be used. Are they satisfied? Can you use Normal Approximation: Yes or No? (b) Find the mean µ and the standard deviation σ for the number of donors in the selected sample that have type A blood. (Keep three decimal places.) µ = σ = (c) Find the probability that more than 2 of the selected donors have type A blood. Use the Normal Approximation. (Do not forget continuity correction!) Draw a diagram. Round off to four decimal places. [Bonus] Find the probability that exactly 2 of the selected donors have type A blood. Use the Normal Approximation. Draw a diagram. Round off to four decimal places. 4

5 Q9 Use the data in the following table, which summarizes blood groups and Rh types for 00 subjects: Type Group O A B AB Rh Rh (a) If a subject is randomly selected, find the probability of getting someone who is group B and type Rh +. (b) If a subject is randomly selected, find the probability of getting someone who is group B or type Rh +. (c) If 2 of the 00 subjects are randomly selected with replacement, find the probability that they are both group B and type Rh +. (Do not apply the 5% guideline. Round off to four decimal places. Show your work.) (d) If 2 of the 00 subjects are randomly selected without replacement, find the probability that they are both group B and type Rh +. (Do not apply the 5% guideline. Round off to four decimal places. Show your work.) 5

6 Q0 Assume that adults have IQ scores that are normally distributed with a mean of 00 and a standard deviation of. Answer the questions below by using Table A-2 or technology (state which method you use). Draw a diagram in each case. (a) Find the probability that the IQ of a randomly selected adult is between 87 and 98. Round off your answers to four decimal places. (b) Find the IQ score separating the bottom 86% from the top 4% of adults. Round off your answers to one decimal place. (c) If 9 adults are randomly selected, find the probability that their average IQ score is at least 99. Use the Central Limit Theorem. Round off your answers to four decimal places. (d) Give the reason why in question (c) you can use the Central Limit Theorem. 6