Suppose that police promotion exam's scores are normally distributed with a mean of 62 and standard deviation of 10. For Questions 3 to 5, use the Critical Value Table B.1, which can be found in the "DATA" section on Blackboard. 1. What is a z-score for an officer getting an exam grade of 50? 2. What is an exam grade for a z-score of 1.5? 3. What percentage of the scores falls between a grade of 62 and 77? 4. What percentage of the scores falls below a grade of 77? 5. Officers need to score in the top 10% on the exam in order to be considered for promotion. What is a minimum exam score required for promotion? Assignment 3B: One sample Z-test (10 points) A criminal justice professor wants to see how well his current class (CJUS3312) is performing. The average grade in his current class of 49 students is 83. In the past 20 semesters/quarters that the professor has taught CJUS3312, the average performance in the class was 79 with a standard deviation of 16. Take this as the population values. He hypothesizes (H1) that the mean performance/grade in his current class is greater than the previous classes; that is, this current class are genuinely smarter. Using the 0.05 significance level, test the null hypothesis (H0) that the current class is the same as the previous classes (i.e., there is no difference between the current class and previous classes). IMPORTANT: Do not to round intermediate calculations. If it's necessary, round it to 5 decimal places. 1. Is the research hypothesis one-tailed or two-tailed? 2. Calculate the test statistic (obtained value). 3. Can you reject the null hypothesis? EXPLAIN WHY (in one sentence). *Be sure to write the critical value. Use the Critical Value Table B.1, which can be found in the "DATA" section. 4. Interpret your answer for Q3 (in one sentence). 5. Can you reject the null hypothesis at the 0.01 significance level? Interpret your