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 ​​ and ​​.

(type integers or decimals. do not round.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule for a normal distribution states that approximately 99.7% of the data lies within \( \mu\pm3\sigma\).

Step2: Calculate the lower and upper bounds

Given \(\mu = 100\) and \(\sigma=10\).
For the lower bound: \( \mu - 3\sigma=100 - 3\times10=100 - 30 = 70\).
For the upper bound: \( \mu+3\sigma=100 + 3\times10=100 + 30 = 130\).

Answer:

The central 99.7% of the IQ scores are between \(70\) and \(130\).