Question

The IQs of a population are normally distributed with a mean of 100 and a standard deviation of 18.

a) What is the probability of a person selected at random having an IQ greater than 109?

b) What is the probability that a random sample of 20 people will have a mean IQ greater than 109?

Answer 1

Solution :

Given ,

mean = = 100

standard deviation = = 18

P(x >109 ) = 1 - P(x< 109)

= 1 - P[(x -) / < (109-100) /18 ]

= 1 - P(z <0.5 )

Using z table

= 1 - 0.6915

= 0.3085

probability=0.3085

(B)

n = 20

= 100

= / n = 18/ 20 = 4.0249

P( >109 ) = 1 - P( <109 )

= 1 - P[( - ) / < (109 -100) /4.0249 ]

= 1 - P(z <2.24 )

Using z table

= 1 - 0.9875

= 0.0125

probability= 0.0125