SOCI301_Assignment4_LessardNicholas_3418175

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Athabasca University, Athabasca *

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Sociology

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Jan 9, 2024

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1. (5 marks) The distribution of the number of Halloween treats consumed on Halloween night has a mean of 10 and a standard deviation of 6. Z=X-M/SD a. What is the Z score for a child eating 20 treats? 20-10/6 = 1.67 b. What is the Z score for a child eating 5 treats? 5-10/6 = -0.83 c. How many treats were eaten by a child with a Z score of −1.5? X=(Z)(SD)+M (-1.5)(6)+10 = 1 d. What percentage of children ate 15 or more treats? 15-10/6 = 0.83 Percentage of children who ate 15 or more treats according to the normal curve table in table A-1 in the textbook is 20.33% when looking at the % in the tail with a Z score of 0.83. 2. (7 marks) A distribution of exam scores in Sociology 100 for the past five years has a mean of 75 and a standard deviation of 20. a. What is the Z score for a person who achieved 90? 90-75/20 = 0.75 b. What is the Z score for a person who achieved 40? 40-75/20 = -1.75 c. What percentage of students earned a grade of 80 or better? 80-75/20 = 0.25 d. What range of values represents the middle 75% of the distribution? If looking for the middle 75% of the distribution we would need to find where the top 12.50% ends and the bottom 12.50% begins. Using the normal curve table in table A-1 in the textbook, the closest percentage to 12.50% is a percentage in the tail of 12.51% with Z score of 1.15 and -1.15 for symmetry. X = (Z)(SD) + M (1.15)(20)+75 = 98 (-1.15)(20)+75 = 52 A value of 52 to 98 would represent the middle 75% of the distribution. 3. (4 marks) You are conducting a survey at a college with 800 students, 50 faculty members, and 150 administrative staff members. Each of these 1,000 individuals has a single listing in the campus phone directory. Suppose you were to cut up the directory and pull out one listing at random to contact. What is the probability it would be a. a student? 800/1000 = 0.8 = 80%

b. a faculty member? 50/1000 = 0.05 = 5% c. a faculty or administrative staff member? 50+150 = 200/1000 = 0.2 = 20% 4. (4 marks) You apply to 20 graduate programs, 10 of which are in the United States, 5 of which are in Canada, and 5 of which are in Australia. You get a message from home that you have a letter from one of the programs you applied to, but nothing is said about which one. Give the probability that it is from a. a program in the United States. 10/20 = 0.5 = 50% b. a program in Canada. 5/20 = 0.25 = 25% c. any program other than one in Australia. 10+5 = 15/20 = 0.75 = 75%

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