Reference no: EM132580741

Q1. The Empirical Rule is based on the standardized normal distribution. 

a) Describe how you could use the Empirical Rule to evaluate the distribution of scores on a national test. You are given the following information for the national test: (1) the population mean = 450 and (2) the population SD = 75.

b) Second, based on the information given above, estimate the range of scores on this test. That is, estimate the low score and the high score on the test. Discuss how you arrived at your estimate for each score.

c) Finally, determine where students' test scores on the national test would place them in terms of their percentile ranking. You are given the following information on test scores of three students.

d) Student A scored a 600. What percentile is this student?

e) Student B scored a 225. What percentile is this student?

f) Let's say a student's score placed them in the 99th percentile. Estimate the student's score using whatever means gives you a good estimate.

Q2. You should be familiar with the concept of using the z-formula to calculate probabilities for values that cannot be solved neatly with the Empirical Rule. Recall several examples of how the z-calculation was used to determine the proportion of a certain salary range (refer to slides 7-8 through 7-14). The population mean for salaries was $1100, and the population standard deviation was $80. Please answer the following questions. Be sure to show your work.

a) What percent of salaries range from $1100 to $1200?

b) What percent of salaries are below $950? What percent of salaries range from $1050 to $1250?