Question

a particular iq test is standardized to a normal model, with a mean of 100 and a standard deviation of 10.
part 4 of 5
points: 0 of 10
choose the model for these iq scores that correctly shows what the 68 - 95 - 99.7 rule predicts about the scores.
a.
b.
c.
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.
about what percent of people should have iq scores above 130?
using the 68 - 95 - 99.7 rule, about.15% of people should have iq scores above 130.
about what percent of people should have iq scores between 90 and 100?
using the 68 - 95 - 99.7 rule, about □% of people should have iq scores between 90 and 100.
(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 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 \( \sigma=10\).

Step2: Analyze the interval 90 - 100

We know that \( \mu-\sigma=100 - 10=90\) and \( \mu = 100\). The interval from \( \mu-\sigma\) to \( \mu\) is half of the interval \( \mu - \sigma\) to \( \mu+\sigma\). Since the interval \( \mu-\sigma\) to \( \mu+\sigma\) contains 68% of the data, the interval \( \mu-\sigma\) to \( \mu\) contains \( \frac{68\%}{2}=34\%\) of the data.

Answer:

34