statistics?

Question

assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15(as on the wechsler test)(draw a graph)
finad the probability that a randomly selected adult has an IQ greater than 131.5(the requierment for membership in the Mensa organization)

Answer 1

The IQ score you are looking for is 2.1 standard deviations above the mean (z = 2.1). Thus, approximately 1.8% of the population would be expected to have an IQ score of 131.5 or higher.

Answer 2

Hi,
The answer is: .0179 rounded to three decimal places.
First I’ll do it the “hard” way and then the easy way.
a) First ind the z-score.
z=(x-bar –x)/σ (I’ve used x-bar for the mean because I don’t know how to make an x with a bar over it.)
z=(131.5-100)/15
=2.1
b) Look up the area in the normal distribution tables:
area = 0.4821
c) Now, subtract that from the total area to the right of the mean, that’s 0.5, of course.
0.5-.4821=0.0179

Now the easy way using a TI-83 Plus/TI-84 or similar calculator.
a) Press 2nd , VARS, 2 and normalcdf( will be pasted to the home screen.
b) Enter your numbers according to the following syntax: normalcdf(left bound, right bound, mean, std. dev.) If your problem this would be normalcdf(131.5, 1E99, 100, 15)
c) Press ENTER and the answer 0.0178643… will be displayed.
Note that I used 1E99 for the right bound. That’s essentially at infinity. The E is gotten by pressing 2ND and then the comma key.

FE