Question

Statistics Assignment 17 1) Find the upper and lower -Scores for the middle 50% of a normal distribution. What percentiles do these numbers represent? 22101 2.61 2) What is the range of z-scores that are outliers for the normal distribution? 2.63 X 3) The Wechsler IQ test is designed to assess human intelligence. I should start by waming you that a lot of people think IQ tests are totally bogus. The Wechsler test is designed to be normally distributed with a mean of 100 and a standard deviation of 15. a) Determine the score at the 25th percentile. 100-.07.15 (90 b) Determine the score at the 75th percentile. 100+. 67.5 670 10 c) Suppose that a person is considered a genius if his/her score is an outlier on the high end. What score would be an outlier? 100+ 2.68. LIS) (140 d) What proportion of the population are "geniuses by this definition? e) There are 1800 students at this school. How many geniuses would you expect?

if someone could give an explanation for D. the answer is 0.37%. I would just like to know how they got that answer in steps.

Answer 1

IS is An observation is outlier if 1217 2.68 a, b, c are corred. Since, you have asked for (d) part. 2) A person is genius il he in outlier on high end let & be score of wechsier test XNN 1100, (15,2) xo 100 ~ N(0,1) Person is genius if x - 100 79.68 Now proportion of the population who are genius = P(x - 100 > 2.68) = P(z > 2.68)= - 0 (2.60) = 1- 0.9963 = 0.0037 il 0.37 % of the population are genius. (el = 1800 1800+ 0.0037 expected No ol genius people = 15 = 6.66 N 7