Suppose z is the standard normal variable. Draw the normal curve for each of the following probability statements to visualize the required area. Report answers accurate to at Ieastdl decimal places. a.P{-2.34 1.5 and z r; 4125} = C] c.P{z c4128 and g g 1.56)= C] d.P{z :3 1.5 m' z :3 [L57] = C] e.P{z f. 1.53 or z }1.59}= C] f.P{z:>l184 given 22>D) = C] g.P{z >1.5 given 2 s 0.11;. = C] h. Pp: >425 given 2 e 0.57:. = C] Question Help: ElVideo a Read E Message instructor \fFor which of the following pairs of significance levels and p-values are the results statistically significant? That is, for each a should Ho be rejected based on the given p- Value? Select all cases where Ho should be rejected: Da = 0.005; p-value = 0.092 Da = 0.100; p-value = 0.043 Da = 0.025; p-value = 0.174 Da = 0.010; p-value = 0.006 Da = 0.001; p-value = 0.011 Da = 0.050; p-value = 0.002On a peertopeer {P2P} lending website, borrowers complete an approval scoring form that lenders use to assess creditworthiness. Lenders gen emlly believe that borrowers who score at least 13 do not default on loans. Consequently, borrowers are rated A if their overall score is at least T3, otherwise they are rated E. .5. reasonably large sample of real borrower data was collected: i. among those that did not default on their loansr initial approval scores were normally distributed with a mean of TE? and a standard deviation of 13. ii. among those that defaulted on their loa nsI initial approval scores were normally distributed with a mean of EB and a standard deviation of 3.2. Report each answer as a decimal [not percent) accurate to at least 4 decimal places. Answers from software or from rounded zscores [to 2 decimal places] are accepted. 1. 1ll'll'hat proportion of borrowers that: a) defaulted were initially rated A? C] b) did not default were initially rated E? [j c} defaulted were miscategorized initially? C] cl) did not default were miscategorized initially? C] 2. Among those that defaulted, what is the probability that a borrower: a) scored above 67.5? bj scored below 66.1 or above 73.6? c) was rated B and scored above 46.2? d) was rated A and scored below 67.5? e) was rated A given scored above 68? f) scored below 68 given rated B? uestion Help: & Message instructor Submit QuestionOn a peer-to-peer {P2P} lending website, borrowers complete an approval scoring form that lenders use to assess credihvorthiness. Borrowers are rated :1, B, C or [llr based on their scores, wi'I 15. having the highest scores and D having the lowest. In a large sample of borrowers, 1335 were rated A, 31% were rated E, 34% were rated E, and the rest were rated D. Suppose the scores are norrnaII}.r distributed with a mean of 34S and a standard deviation of 50'. Round numeric answers to the nearest integer. a} What is the cut-off score between .5. and B? b] What is the cut-oft" score between B and C? c} What is the cut-o score between {I and D? DUB cl} What score corresponds to the E'l percentile? e} What score corresponds to- the lth percentile? fjl What is the minimum score above which lies 4% of the scores? C] g} Between what scores will the middle ?'5% of scores lie? Lower value : C] Higher value : C] h] What rating will a score of 3'05 receive? DD i] What rating will a score of 356 receive? II.I'I.I'hich of the following statements about the sampling distribution of the mean {distribution of sample means} and the central limit theorem {CLT] are true'il Select four [4] true statements from the list below: El - From the same population, the standard error of the sampling distribution with n : 39 will be smaller than the standard error Iwith n. : 19. El - The larger the sample sizeI the larger the standard error. El - The smaller the sample size, the smaller the difference between the mean of the sampling distribution and the population mean. El - The sampling distribution is always approximately normal even if the population is not normal. El - From the same population, the mean of the sampling distribution [ail with n : 9 will be equal to the mean with 11 : 1?. El - The shape of the sampling distribution is closer to the population shape as the sample size increases. El - The sampling distribution of the mean will be approximately normal when sample size is large. El - If the population is non-normally distributed, then sample size does not matter for the central limit theorem to apply. El - If p: = p and or: = i, then the distribution of sample means is normal. 11. El - If a population is perfectly normal, then for the distribution of sample means of any size, p3 = p and a", = or. II - The sampling distribution is still assumed to be approximately normal if the underlying population is negatively skewed as long as the sample size is large. Consider a population with a mean 3,: = 19D and standard deviation or = TE. Suppose random samples of size n = 53 are selected from this population. 1. all What is the mean of the distribuon of the sample mean? b} What is the standard error of the mean? [2 decimal places} In the following questions. round the standard error and zscores to exactly; decimal places before determining probabilities. Report probabilities accurate to at least 3 decimal places. 2. What is the probability that a mndornlguI selected sample mean is: all greater than IT'S}? b} less than 185.??? C] 4:} greater than 1?5.'.I" and less tan 1863? [j d} greater than 175.? given less than 1315.??? e] greater than Iii? or greater than 1853? C] 3. Between What values Iivould you expect to nd the middle 730% of the sample means? Round to the nearest integer. Place the smaller value in me rst loox and the larger value in the second box. 3. Between what values would you expect to find the middle 70% of the sample means? Round to the nearest integer. Place the smaller value in the first box and the larger value in the second box. Between and 4. Why are we able to use the normal distribution in the calculations above? O Becasuse the standard error is large enough O Because the sample size is large enough O Because the sample mean is large enough O Because the original population is normal