## Homework 4 Normal Curve And Z Scores Statistics

Psyc 60 - Statistics Homework 4 Remember to follow the homework guidelines listed in the course syllabus. Homework 4 is due at the beginning of class on Wednesday, May 1st.----------------------------------------------------------------------------------------------------------------1. What proportion of a normal distribution is located between each of the following z-score boundaries? a. z = -0.50 and z = 0.05 0.1915 + 0.0199 = 0.2114 b. z = -0.90 and z = 0.90 0.3159 + 0.3159 = 0.6318 c. z = -1.50 and z = 1.50 0.4332 + 0.4332 = 0.8664 2. For a normal distribution with a mean of 80 and a standard deviation of 20, find the proportion of the population corresponding to each of the following scores. a. Scores greater than 85; z = 0.25; 0.4013 b. Scores less than 100; z = 1; 0.8413 c. Scores between 70 and 80 z = -0.5; 0.1915 3. For each of following statements, sketch a normal curve and shade the target area. Then, find the proportion of the total area identified by each statement. a.

PSYC 354 H OMEWORK 5 Z-Scores Be sure you have reviewed this module/week’s lessons and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, and then copy and paste your output and graphs into your homework document file. Number all responses. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Review the “Homework Instructions: General” document for an example of how homework assignments must look. Part I: Concepts These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. 1. What are always the mean and standard deviation of the z-distribution? 0 and 1 2. Define the central limit theorem. The central limit theorem refers to how a distribution of sample means is a more normal distribution than a distribution of scores, even when the population distribution is not normal. 3. Fill in the blanks: A z-score is based on a distribution of _____ standard score ________, while a z-statistic is based on a distribution of _______ mean ___________. 4. End-of-chapter problems: Remember to show work to receive partial credit where applicable. For help working on these problems, refer to the presentation from this module/week on the normal curve and computing z-scores. Raw and z-scores: 6.16 and 6.20 6.16 If a population has a mean of 250 and a standard deviation of 47, calculate z scores for each of the following raw scores: a. 391 z = (391-250)/47 = 3.0 b. 273 z = (273-250)/47 = 0.49 c. 199 z = (199-250)/47 = -1.09 d. 160 z = (160-250)/47 = -1.91 6.20 For a population with a mean of 250 and a standard deviation of 47, convert each of the following z scores to raw scores. a. 0.54 x = .54(47) + 250 = 275.38 b. -2.66 x = -2.66(47) +250 = 124.98 c. -1.0 x = -1.0(47) +250 = 203 Page 1 of 9

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