Question

The Wechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of WAIS scores for persons over 16 years of age is approximately normal with mean 100 and standard deviation 15. Use the 68–95–99.7 rule to answer these questions.

(a)

What is the probability that a randomly chosen individual has a WAIS score of 115 or higher?

(b)

In what range do the scores of the middle 95% of the adult population lie?

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 15

a) P(x > 115) = 1 - p( x< 115)

=1- p P[(x - ) / < (115 - 100) /15 ]

=1- P(z < 1.00)

Using z table,

= 1 - 0.8413

= 0.1587

Using Empirical rule,

b) P( - 2 < x <   + 2 ) = 95%

= P( 100 - 2 * 15 < x < 100 + 2 * 15 ) = 95%

= P( 100 - 30 < x < 100 + 30 ) = 95%

=P( 70 < x < 130 ) = 95%

95% middle is range 70 to 130