Could you explain how to solve following questions as in detail as possible :

Question numbers: 3,4,7,8,9,11,12

I could not understand how to solve these questions.

WRI'I'I'EN ASSIGNMENT UNIT 8 Estimating the EXpectation A measurement follows the normal distribution with a standard deviation of 15 and an unknown expectation p. You can consider that measurement to be the "original" distribution. Two statisticians propose two distinct ways to estimate the unknown quantity u with the aid of a sample of size 36. They will do that by evaluating two different SAMPLING DISTRIBUTIONS to determine which method is better. There are two statisticians involved in this task: statistician "A" and statistician "B." Statistician A proposes to use the sampling distribution of the sample average as an estimate. Statistician B proposes to use the sampling distribution of the sample median instead. In order to choose between the two options they agree to prefer the statistic that has a smaller variance (with respect to the sampling distribution). Tasks 1-9 refer to this problem of comparing the two statistics to each other. Question 1 Assume that the actual expectation of the measurement is equal to 5 (p:5). Then the expectation of the statistic that was proposed by Statistician A is equal to: Answer: 5 Feedback The correct answer is: 5 Question 2 Assume that the actual expectation of the measurement is equal to 5 (p:5). Then the standard deviation of the statistic that was proposed by Statistician A is equal to: Answer: 15 Feedback The correct answer is: 2.5 Question 3 Assume that the actual expectation of the measurement is equal to 5 (p:5). Then the expectation of the statistic that was proposed by Statistician B is equal to: (In order to answer this question you may need to conduct a simulation. similar to the simulations This may some was downloaded by 100000x27143m from Connel-Iemcmn on 0573172021 nuns GMT 05:00 imp:,llwwwzaumhcmzam/lrxwlXSNIKITIE'LASSIGNMENTrUNlTidocx/ that are presented in the book. Choose the option closest to the outcome of the simulation.) 13 Select one: a. 2'3 Feedback b. 3.7 The correct answer is: 2.3 c. 4'1 Question 6 d. 5.0 Assume that the actual expectation of the measurement is equal to 2.3 (p=2.3). Then the standard deviation of the statistic that was proposed by Statistician A is equal to: Answer: 15 Feedback The correct answer is: 5.0 Feedback Question 4 The correct answer is: 2.5 Assume that the actual expectation of the measurement is equal to 5 01:5). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: (In Question 7 order to answer this question you may need to conduct a simulation. similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.) Assume that the actual expectation of the measurement is equal to 2.3 (p=2.3). Then the expectation of the statistic that was proposed by Statistician B is equal to: (In order to answer this question you may need to conduct a simulation, similar to the simulations Select one: that are presented in the book. Choose the option closest to the outcome of the a. 2_o simulation.) Select one: b. 2.5 a. Q c. J b. 3.7 d. 3.5 c. 41 Feedback The correct answer is: 3.0 Feedback Question 5 The correct answer is: 2.3 Assume that the actual expectation of the measurement is equal to 2.3 (p=2.3). Then the expectation of the statistic that was proposed by Statistician A is equal to: Question 8 Tins study some was dow-doedod by 10000082714362!) from Counccmcnm on 05314021 000133 GMT 05:00 This study some was dow-doedod by 10000082714362!) from Counccmcnm on 05314021 000133 GMT 05:00 htlps.llwwwzaumhcmzom/lrxwlXB/WRITIE'LASSIGNMENTVUNITGdocx/ htlps,llwwwzaumbcmzom/lrxwlXSNIRmrASSIGNMENTVUthidocx/ Assume that the actual expectation of the measurement is equal to 2.3 (u=2.3). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: (In order to answer this question you may need to conduct a simulation. similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.) Select one: a. 2.0 b. 2.5 04) d. 3.5 Feedback The correct answer is: 3.0 Question 9 Based on the information collected in Tasks 1-8. which of the two statistics produces values which tends to be more concentrated about the expectation of the measurement? Select one: a. The statistic proposed by Statistician A b. The statistic proposed by Statistician B Feedback The correct answer is: The statistic proposed by StatisticianA Information Normal Approximation of the Sampling Distribution of a Sum Suppose that the expected number of phone calls that are handled by a switchboard in each second is 5.35. Assume that the distribution of the number of phone calls per second follows the Poisson distribution. Tasks 10-12 refer to this information. Question 10 The number of phone calls that the switchboard is expected to handle in 1 minute is Answer: [321 Feedback The correct answer is: 321 Question 11 The 0.80-percentile of the number of calls per minute is (approximately) equal to: (Use the Normal approximation. The answer may be rounded up to 3 decimal places of the actual value.) Answer: 336.0789 Feedback The correct answer is: 336.0789 Question 12 The probability that the switchboard will need to handle no more than 300 call in a minute is: (Use the Normal approximation. without a continuity correction. The answer may be rounded up to 3 decimal places of the actual value.) Answer: l 0.1205773 Feedback The correct answer is: 0.1205773 Thu study some was downloaded by 10000082714362!) from Counccmcom on 05314021 000133 GMT 05:00 Thu study some was downloaded by 10000082714362!) from Counccmcom on 05314021 000133 GMT 05:00 Imps.llwwwmumhcmmm/lrxwlXBNIRnTDLASSIGNMENTUNITdocxI Imps.llwwwmumbcmmm/lrkwlXS/WRITIDLASSIGNMENTVUNIT1MDCXI