MATH 1280 Self-Quiz Unit 7 (100%) – University of the People | MATH 1280 Self-Quiz Unit 7 (100%)

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MATH 1280 Self-Quiz Unit 7 (100%) – University of the People Grade 10.00 out of 10.00 (100%) Top of Form Information text Recall that the population average of the heights in the file "pop1.cs... v" is μ = 170.035. Using simulation it can be shown that the probability of the sample average of the height falling within 2 centimeter of the population average is approximately equal to 0.925. From the simulations we also got that the standard deviation of the sample average is (approximately) equal to 1.122. In the next 3 questions you are asked to apply the Normal approximation to the distribution of the sample average using this information. The answer may be rounded up to 3 decimal places of the actual value: Question 1 Correct Question text Using the Normal approximation, the probability that sample average of the heights falls within 2 centimeter of the population average is Answer: Question 2 Correct Question text Using the Normal approximation we get that the central region that contains 90% of the distribution of the sample average is of the form 170.035 ± z · 1.122. The value of z is Answer: Question 3 Correct Question text Using the Normal approximation, the probability that sample average of the heights is less than 169 is Answer: Question 4 Correct Question text According to the Internal Revenue Service, the average length of time for an individual to complete (record keep, learn, prepare, copy, assemble and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is 2 hours. Suppose we randomly sample 36 taxpayers and compute their average time to completing the forms. Then the probability that the average is less than 10 hours is approximately equal to (The answer may be rounded up to 3 decimal places of the actual value) Answer: Information text Suppose that a category of world class runners are known to run a marathon (26 miles) in an expectation of 145 minutes with a standard deviation of 14 minutes. Consider 49 random races. In the next 3 questions you are asked to apply the Normal approximation to the distribution of the sample average using this information. The answer may be rounded up to 3 decimal places of the actual value: Question 5 Correct Question text The probability that the runner will average between 143 and 145 minutes in these 49 marathons is Answer: Question 6 Correct Question text The 0.90-percentile for the average of these 49 marathons is Answer: Question 7 Correct Question text The inter-quartile range of the average running time is Answer: Question 8 Correct Question text The time to wait for a particular rural bus is distributed uniformly from 0 to 25 minutes. 25 riders are randomly sampled and their waiting times measured. The 90th percentile of the average waiting time (in minutes) computed for the sample is (approximately): Select one: a. 210.0 b. 26.9 c. 14.3  d. 13.2 Information text A switching board receives a random number of phone calls. The expected number of calls is 7.4 per minute. Assume that distribution of the number of calls is Poisson. The average number of calls per minute is recorded by counting the total number of calls received in one hour, divided by 60, the number of minutes in an hour. In the next 4 questions you are asked to apply the Normal approximation to the distribution of the sample average using this information. The answer may be rounded up to 3 decimal places of the actual value: Question 9 Correct Question text The expectation of the average is Answer: Question 10 Correct The standard deviation of the average is Answer: Question 11 Correct The probability that the average is less than 7 Answer: Question 12 Correct Question text The probability that number of calls in a random minute is less than 7 is Answer. (Note, the question is with resect to a random minute, and not the average.) Information Information text It is claimed that the expected length of time some computer part may work before requiring a reboot is 3.5 months. In order to examine this claim 70 identical parts are set to work. Assume that the distribution of the length of time the part can work (in months) is Exponential. In the next 4 questions you are asked to apply the Normal approximation to the distribution of the average of the 70 parts that are examined. The answer may be rounded up to 3 decimal places of the actual value: Question 13 Correct The expectation of the average is Answer: Question 14 Correct The standard deviation of the average is Answer: Question 15 Correct Question text The central region that contains 90% of the distribution of the average is of the form E(X) ± c, where E(X) is the expectation of the sample average. The value of c is Answer: Question 16 Correct Question text The probability that the average is more than 4 months is Answer: Bottom of Form [Show More]

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