Please show all the necessary solutions.

I.

Find the unknown constant a given the area under the standard normal curve: Use the z-table provided in Study Guide 6. Express your answers in 2 decimal places. A. P (Z a) = 0.8980,a = C. P(Z a) = 0.4980, a = E. P(a 22) : C. Probability that the customer will have to wait less than 18 mins or more than 25 mins: 1 Is it likely that a person will be seated in less than 15 minutes? The probability that a person will be seated in less than 15 minutes is . Thus, it is (write either likely or unlikely_, in lowercase letters) to be seated in less than 15 minutes. Problem 2 A professor gives a 100-point examination in which the grades are normally distributed. The mean is 60 and the standard deviation is 10. If there are 5% A's and 5% F's, 15% B's and 15% D's, and 60% CS, nd the scores that divide the distribution into those categories. Note: the scores must be from 0 to 100 and must be whole numbers since the exam given is 100 items and worth 1 point each. 50, round up; your answers to the nearest whole number. A is the highest grade, F is the lowest. The interval of scores for Grade A: [ 100] The interval of scores for Grade B: [ The interval of scores for Grade C: [ The interval of scores for Grade D: [ The interval of scores for Grade F:A top 3% of students receive Php25,000. What is the minimum score you would need to receive this award? A. z-value corresponding to top 3%: B. The minimum score you would need to receive the award: Problem 3 A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. Round off z-values to two decimal places. Round up the scores to whole numbers. The bottom 1.5% of students must go to summer school. What is the minimum score you would need to stay out of this group? A. zvalue corresponding to bottom 1.5%: B. The minimum score you would need to stay out ofthe group