Statistics and Probability

Problem Set 5 Chapter 2 - Lesson 6: Application of Normal Distribution Instructions: With your Partner, solve the following problems and show your complete solution. Draw the normal curve then shade the needed are and indicate the z-value. 1. Given that x is a normal distribution random variable with the mean of 50 and a standard deviation of 5, find the following: A. B. C. 2. Based on the records of the Admissions Office of University X, the mean score of all Grade 11 test-takers is 120 with a standard deviation of 20. Assuming that the scores are normally distributed, answer the following problems. A. What is the z-score of a certain student whose raw score is: a. 120? b. 112? C. 130? B. What is the raw score of a certain student whose z-score is equivalent to: a. 3? b. 2.5? C. -1.50? C. What is the probability that a randomly selected student is one of the students whose scores are between 90 to 140? D. Assuming that there were 2,000 test takers, how many of the students have scores that are: a. Greater than 140? b. Less than 120? C. Between 130 and 165? d. Between 85 and 112