Question

a particular iq test is standardized to a normal model, with a mean of 100 and a standard deviation of 10.
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 15% of people should have iq scores above 130.
(type an integer or a decimal. do not round.)
d) about what percent of people should have iq scores between 90 and 100?
using the 68 - 95 - 99.7 rule, about 34% of people should have iq scores between 90 and 100.
(type an integer or a decimal. do not round.)
e) about what percent of people should have iq scores above 110?
using the 68 - 95 - 99.7 rule, about % of people should have iq scores above 110.
(type an integer or a decimal. do not round.)

Explanation:

Step1: Analyze the position of 110

Given mean \(\mu = 100\) and standard deviation \(\sigma=10\). For \(x = 110\), \(z=\frac{x-\mu}{\sigma}=\frac{110 - 100}{10}=1\).

Step2: Use the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule states that about 68% of the data is within \(\mu\pm\sigma\), 95% within \(\mu\pm2\sigma\), and 99.7% within \(\mu\pm3\sigma\). The percentage of data above \(\mu+\sigma\) is \(\frac{100 - 68}{2}=16\%\)

Answer:

16