Answer with problem

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). Find the probability that a randomly selected adult has an IQ between 90 and 120

Answer 1

For this question, you are looking for the area under the curve between the values 90 and 120 for this distribution.

The area between the values is the area to the left of 120 - area to left of 90. We can find the area to the left of the values by computing the Z scores for each value and looking these up on a normal distribution table.

z= x - (mean)/std. dev

so Z for 90= (90-100)/15 = -.67

z for 120 = (120-100)/15 = 1.33

From the normal table, area to left of 120 (z=1.33) = .9082; area to left of 90 (z = - .67) = .2514

so area between = .9082-.2514= .6568. Remember area under the curve corresponds to probability.

Another way to do this is you are allowed to use a graphing calculator such as the TI-83/4 is to use the Distribution functions

for TI, you would hit the 2nd key then the VARS/distr key (to the left of clear)

go to normal cdf

you can then enter the upper and lower limits as well as the mean and standard deviation for the distribution so you do not need to convert the values to Z values.

so you would enter

Lower: 90

Upper:120

µ = 100

σ = 15

then Paste, enter

it returns the area/probability .6563. This will be slightly different than the table values as the calculator will carry Z values to more than 2 decimal places.