Question

3) The scores of adults on a IQ test are approx deviation 12. adults on a IQ test are approximately normal with mean 100 and standard a. What proportion of adults have an IQ below 90? b. What proportion of adults have an IQ above 115? c. What proportion of adults have IQ between 85 mm and 105 mm? d. Which is the IQ if the group of adults having 30 % of the population with an IQ below them. 4) Consider following scatterplot: 10 20 Make a short analysis of this correlation. What can you say about the relations of these two variables? Give a possible narrow range of values for the correlation index.

Answer 1

3) a) P(X < 90)

= P(z < (90 - 100)/12)

= P(z < -0.83)

= 0.2023

b) P(X > 115)

= P(z > (115 - 100)/12)

= P(z > 1.25)

= 0.1056

c) P(Between 85 < X < 105)

-pr85 -100 ー 、 105 - 100、 < < 12 12

= P(-1.25 < z < 0.42)

= 0.5559

d) z score corresponding to 30% area to its left = -0.52

Hence,

Required IQ = 100 - 0.52*12 = 93.76

4) The points are very closely following a straight line which is negatively sloped and there is not much deviation of any point from this path which indicates that there is no outlier in the data. The variables are having strong negative relationship. The correlation coefficient should be between -0.7 and -0.9