Question

a particular iq test is standardized to a normal model, with a mean of 100 and a standard deviation of 10.
a) choose the model for these iq scores that correctly shows what the 68 - 95 - 99.7 rule predicts about the scores.
b) in what interval would you expect the central 99.7% of the iq scores to be found?
using the 68 - 95 - 99.7 rule, the central 99.7% of the iq scores are between 70 and 130.
(type integers or decimals. do not round.)
c) about what percent of people should have iq scores above 130?
using the 68 - 95 - 99.7 rule, about □% of people should have iq scores above 130.
(type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule for a normal distribution states that about 99.7% of the data lies within \( \mu\pm3\sigma\). Given \( \mu = 100\) and \( \sigma=10\), then \( \mu + 3\sigma=100 + 3\times10=130\) and \( \mu-3\sigma=100 - 3\times10 = 70\). The total percentage of data is 100%.

Step2: Calculate the percentage above 130

Since the normal distribution is symmetric, the percentage of data outside of \( \mu\pm3\sigma\) is \(100\% - 99.7\%=0.3\%\). This \(0.3\%\) is split evenly between the two tails (the part less than \( \mu - 3\sigma\) and the part greater than \( \mu+3\sigma\)).

Answer:

\(0.15\)