Graded Quiz Unit 6 - Selection of my best coursework PDF

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Selection of my best coursework...

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MATH 1280 GRADED QUIZ UNIT 6 UNIVERSITY OF THE PEOPLE Started on

Sunday, 7 March 2021, 3:16 AM

State

Finished

Completed on

Sunday, 7 March 2021, 4:00 AM

Time taken

44 mins 6 secs

Marks

20.00/20.00

Grade

100.00 out of 100.00

Quiz Instructions: All multiple choice answers are assumed to be rounded to the precision shown, with the last digit being within ± 1. Choose the best answer. There are 20 questions on this test, but you will see only about 4-6 questions on each screen. Information For items 1-4, use the distribution of the random variable Y as show in this table: Value Probability

-4 .08

0 .13

Question1 The missing probability value is: a. .14 b. .05 c. .22 d. .18 e. can not be determined Question2 P(Y < 3) is equal to: a. .08 b. .13 c. .21 d. .37 e. .63 Question3 The expectation of Y, E(Y), is: a. 0.17 b. 0.50 c. 2.00

2 .16

6

9 .19

11 .22

d. 5.45 e. 6.00 Question4 The standard deviation of Y (rounded to two decimal places) is: a. 4.29 b. 4.53 c. 4.71 d. 5.45 e. 6.00 Information: Random variable Z represents the number of successes observed in 500 repetitions of an experiment that has a probability of success of .4 (i.e. the chance of success is 40% for each of the 500 independent experiments). Using this information, determine the following values for the next 5 questions: Question5 P(Z = 240), in other words, the probability that there were EXACTLY 240 successes in the 500 trials (round your answer to 2 decimal places): a. .00 b. .01 c. .03 d. .13 e. .53 Question6 P(Z ≤ 240), in other words, the probability that Z is less than or equal to 240 (rounded to two decimal places) is: a. .00 b. .48 c. .62 d. .97 e. 1.00 Question7 P(220 ≤ Z ≤ 260) is (choose the best answer): a. .04 b. .13 c. .75 d. .86 e. .91 Question 8 The expected number of successes (the expectation) is: a. 0 b. sqrt( sum(Z – 300)^2 / 500) c. 200 d. 240 e. 260

Question9 The population standard deviation of Z is: a. 300 ± 1.683 * z b. 10.95 c. 12.00 d. 30.00 e. sqrt(200) There is a total of 20 questions on this quiz. You are at the half-way point. Information Let X be the amount of time (in minutes) a postal clerk spends with his or her customer. Assume that X has an exponential distribution and that the expectation is: E(X) = 5 minutes (meaning the expected amount of time spent with a customer is 5 minutes). The next 3 questions refer to this waiting time. Question 10 The rate (λ) is equal to:) is equal to:) is equal to:) is equal to: a. 0 b. .20 c. (1/5) / n d. sqrt (5/n) e. 5 Question11 The probability that a clerk spends between four and five minutes with a randomly selected customer (rounded to two decimal places) is: a. .00 b. .01 c. .03 d. .06 e. .08 Question12 The probability that a clerk spends MORE than 10 minutes with a customer is: a. .01 b. .14 c. .87 d. .91 e. .95 Information There are two Poisson distributions: A and B. The distributions are used to model the number of successes in experiments A and B respectively. The expectation of A is 11 and the Expectation of B is 13. Remember that the Poisson distribution is a discrete distribution, so you have to be careful of the difference between “less than or equal to” versus “less than” (and similar distinctions). Question 13 What is the variance of distribution A?

a. sqrt(11) b. sqrt(11) / n c. 11 / sqrt(n) d. 2.71 e. the expectation Question14 What is the probability of getting exactly 13 successes in experiment B? a. .01 b. .11 c. .17 d. .23 e. .95 Question15 What would be the probability of getting MORE THAN 15 successes in a experiment B? a. .24 b. .66 c. .71 d. .75 e. .77 Question16 Which R command would give us an estimate of the width of the range of the middle 90% of observations for distribution A (i.e. find the top and bottom value in the central 90% and find the difference between those two numbers). a. qpois(.05, 11) - qpois(.95, 12) b. ppois(15, 11) - ppois(12, 15) c. qpois(.95, 11) - qpois(.05, 11) d. ppois(.05, 13) - ppois(.95, 13) e. (15 - 12) / (sd(A) + sd(B)) Information The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6.8 days and a standard deviation of 1.7 days. The next 4 questions correspond to this information. Question 17 What is the probability that recovery time is less than 7 days? a. .03 b. .21 c. .24 d. .55 e. .70 Question 18 What is the z-score for a patient who takes 7 days to recover? (Choose the closest possibility.) a. 0.12 b. 0.30 c. 2.10

d. 1.40 e. 0.80 Question 19 What is the probability of spending more than 3 days in recovery? (Choose the closest possibility.) a. 1/3 b. .92 c. .07 d. .95 e. .99 Question 20 The 90th percentile for recovery times is? a. 7.8 b. 8.2 c. 8.6 d. 9.0 e. 11.1...