Assume that IQ scores are normally distributed with a standa

Assume that IQ scores are normally distributed, with a standard deviation of 17 points and a mean of 100 points. If 100 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points? (Round your answer to four decimal places.)

Solution

SOl)

for a sample of a fixed size n,
z = (x - ) /s
where s = n
and n is the sample size
and x is the sample mean, is the population standard deviation and is the population mean.

given:
n = 100
= 17
x - 2 (should not differ by more than 2)

therefore;
s = / n = 17 /100 = 1.7
z = (x - ) /s = 2 / 1.7 = 1.176

P( x - 2 )

=P(z 1.176 )

= 0.5 + P(0<Z<1.176)

use the z-score index table or other calculators;

=0.5 +0.379

=0.879

probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.879