1.IthasbeenfoundthatIQscoresarenormallydistributedwithameanof108andastandarddeviationof16points.(20points)a.WhatistheproportionofpersonswithanIQscoreof80pointsorless?(5points)b.Whatistheprobabilitythataperso

Question

1.It has been found that IQ scores are normally distributed with a mean of 108 and a standard deviation of 16 points.(20 points)
a.What is the proportion of persons with an IQ score of 80 points or less?(5 points)
b.What is the probability that a person randomly chosen will have an IQ score between 100 and 120 points?(5 points)
c.A person must score in the upper 2% of the population in an IQ test to qualify for membership in Mensa (the international high-IQ society).What is the minimum score that one has to achieve in order to qualify for Mensa?(5 points)
d.What is the maximum number of points that a person in the lowest 25% of the IQ population can score?(5 points)

Answer 1

You probably need a table on normal distribution to do this.
a.
(80 -108)/16 = -28/16 = -1.75σ
The area between 0 and -1.75σ is 0.4599
the proportion of persons with an IQ score of 80 points or less is 0.5 - 4599 = 0.0401
b.
(100 - 108)/16 = -0.5σ,the area between 0 and -0.5σ is 0.1915
(120 - 108)/16 = 0.75σ,the area between 0 and 0.75σ is 0.2734
They (100 and 120) are on opposite side of the average,the probability that a person randomly chosen will have an IQ score between 100 and 120 points is 0.1915 + 0.2734 = 0.4649
c.
the percentage of people below the average is 50%,so we need to find out which σ corresponds to 0.48 on the right side of the average.From the table,the value is between 2.55σ and 2.56σ
2.55σ:2.55*16 + 108 = 148.8
2.56σ:2.56*16 + 108 = 148.96
the minimum score is 149
d.
Between 25% and average,the probability is 0.5 - 0.25 = 0.25
0.25 corresponds to a value between 0.67σ and 0.68σ
0.67σ:108 - 0.67*16 = 97.28
0.68σ:108 - 0.68*16 = 97.12
the maximum score is 97