1) The cost of childcare in a community is normally distributed with families paying an average of $200 per week with a standard deviation of $50. (a) What childcare cost is ranked 20th percentile? (b) What childcare cost is ranked 90th percentile? (c) What cost is ranked in the bottom quartile? (d) What cost is ranked in the top quartile 2) A program director of a local community college has mandated that students should obtain at least a grade point average (GPA) of 3.5 to be enrolled in an advanced specialty program. The grade point average (GPA) of current students in the basic program is normally distributed with the mean of 2.8 and a standard deviation of 0.8. There were a total 150 students in the program. (a) What percent of the students will be enrolled in the advanced specialty program? How many are these students? (b) Only the top 10% of the students will be awarded a scholarship. What is the least GPA that will qualify a student for the scholarship? How many students will receive the scholarship? (c) About 50% of the GPA will range between what two values around the mean. How many students lies within this range? (d) What grade point average (GPA) is ranked 65th percentile. (e) What percent of the students had a GPA of less than 3.2? How many are these students? (f) What percent of students had a GPA of 3.8 or more? How many are these students? (g) What percent of the students had a GPA between 2.8 and 3.5? How many are these students? (h) What percent of the students obtained a GPA of less than 2.0 or more than 4.5? How many are these students? (i) About 90 students had GPA of less than how much? 3) According to a national survey, an average Canadian makes $32,500 in annual income with a standard deviation of $2,500. However, you believe that residents in your community make more than the national average. To support your claim, you took a random sample of 50 residents from your community and calculated their average income to be $33,000. At 5% significance level, do you have enough statistical evidence to support you claim? (a) State the null and alternative hypotheses. (b) Decide on the statistical method to use. (d) Establish the critical value. (e) Calculate the test value. (f) Make the decision. (g) Find and interpret the p-value.