Question

a particular iq test is standardized to a normal model, with a mean of 100 and a standard deviation of 16.
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 \square and \square.
(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 about 68% of the data lies within \( \mu\pm\sigma\), about 95% lies within \( \mu\pm2\sigma\), and about 99.7% lies within \( \mu\pm3\sigma\). Here, \(\mu = 100\) and \(\sigma=16\).

Step2: Calculate the lower bound

The lower bound is \(\mu - 3\sigma\). Substitute \(\mu = 100\) and \(\sigma = 16\) into the formula: \(100-3\times16=100 - 48=52\).

Step3: Calculate the upper bound

The upper bound is \(\mu + 3\sigma\). Substitute \(\mu = 100\) and \(\sigma = 16\) into the formula: \(100 + 3\times16=100+48 = 148\).

Answer:

The central 99.7% of the IQ scores are between \(52\) and \(148\).