1.) A new large-scale test that is designed to measure work satisfaction in a remote environment is administered to a sample of n = 5,000 individuals in California. Based on the test results, it appears reasonable to assume that the test scores are normally distributed in the population from which the test takers were sampled. Moreover, it appears reasonable to assume that the population has a mean score of = 52 with a standard deviation of = 4 2.) Using the information provided above. Compute the z-score corresponding to each of the following work satisfaction scores for four individuals who took the test (ROUND TO TWO PLACES AFTER THE DECIMAL POINTS): A) X = 40.5, Z = B) X = 53, Z = C) X = 45, Z = D) X = 60, Z = 3.) Of the four individuals who had the most extreme satisfaction score (A, B, C, or D)? Extreme score: b) Of the four individuals who had the most average satisfaction score (A, B, C, or D)? Average score: 4.) In order to be able to compare the performance of test takers on this satisfaction test with their performance on another satisfaction test created by a different group of researchers, it was decided to convert the reporting scale of the test to a new scale with a new distribution having = 100 and = 10. Compute the converted scale scores of the 4 test takers above on the new scale. Scores on the original test scale: 53, 45 [Hint: use your responses to questions 17 to find the new scores]. a) X = 53, Xnew = b) X = 45, Xnew = 5.) The test is now being implemented operationally and the researchers are interested in knowing the probabilities of observing the following satisfaction scores for individual employees in future samples. Using the original population mean score of = 52 with a standard deviation of = 4 and the unit normal table find the following probabilities. a) P (X < 48) = b) P (X > 52) = c) P (47 < X < 55) 6.) Anxiety scores for a population of students during a pandemic follow a normal distribution with a =60 , and = 6. One month into the pandemic anxiety levels are being measured again with samples of students. In the first sample 4 students were chosen at random, in the 2nd sample 25 students were chosen at random, and in the third sample 100 students were chosen at random. 7.) Using the information provided above, find the z-score corresponding to each sample mean of anxiety scores. A) M = 54 for a sample of n = 4, Z = B) M = 62 for a sample of n = 25, Z = C) M = 62 for a sample of n = 100, Z = Which of the three sample means is the most likely to be obtained, A, B, or C? 16 USF students are sampled and their anxiety scores are measured. Using the information above from the population distribution of anxiety scores, answer the following: 1) What is the probability that the sample mean will be greater than 61.25? p = 2) What is the probability that the sample mean will be between 57 and the population mean of 60? p =