Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 16. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 84 and 116​? ​(b) What percentage of people has an IQ score less than 52 or greater than 148​? ​(c) What percentage of people has an IQ score greater than 116​?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	100
std deviation   =σ=	16.000

percentage of people has an IQ score between 84 and 116:

probability =

P(84<X<116)

=

P(-1<Z<1)=68.0%

b)

percentage of people has an IQ score less than 52 or greater than 148​:

P(X<52)+P(X>148)=100-P(52<X<148)=100-P(-3<Z<3)=100-99.7 =0.3%

c)

percentage of people has an IQ score greater than 116:

=P(X>116)=P(Z>1)=16.0%