1. The quantitative part of a national exam is scaled so that the mean score is 500 and the standard deviation is 100. If the distribution of scores is normally distributed (a) what proportion of the students scored between 500 and 682? (b) What proportion scored between 340 and 682? 2. A researcher found that the length of time for five-person student groups to reach a consensus on an sexual harassment policy at the University of Ghana has a normal distribution with u = 2.2 hours and o = 0.25. (a) What is the probability that a randomly selected group of students will reach a consensus on a similar policy in less than 1.5 hours? 3. The annual incomes for TEWU workers in all the public Universities in Ghana are assumed to be normally distributed with u = Ghe18,500 and o = Ghe1,600. (a) What proportion of TEWU workers receive an income greater than Ghe20,000? (b) Less than Ghe15,500? 4. Suppose that TEWU claims that the average annual wage for their members is Ghe22,000 per year but it is suspected that the actual annual wage is less than Ghe22,000. Data collected for a sample of 40 union employees showed a mean wage of Ghe21,250 and s = 702. Using a = 0.05, determine if the assumption is true. 5. A hospital claims that the average length of patient confinement is 5 days. A study of the length of patient confinement of 36 people showed a mean of 6.2 and s = 5.2. Does this data support the hospital's claim? Use a = 0.01