Question

A particular IQ test is standardized to a Normal​ model, with a mean of 100 and a standard deviation of 18. Using the empirical rule, about what percent of people should have IQ scores above 118​? A 5% B 0.3% C 16% D 2.5%

Answer 1

Answer:

Option C) 16%        

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 18

We are given that the distribution of IQ score is a bell shaped distribution that is a normal distribution.

Empirical Formula:

• Almost all the data lies within three standard deviation from the mean for a normally distributed data.
• About 68% of data lies within one standard deviation from the mean.
• About 95% of data lies within two standard deviations of the mean.
• About 99.7% of data lies within three standard deviation of the mean.

We have to find the percentage of data above 118.

$P(x>118)$

$118 = 100 + 18 = \mu + 1(\sigma)$

From empirical rule we can write:

$P(x>118)\\=50\%-\dfrac{68\%}{2}\\\\=16\%$

Thus, the correct answer is

Option C) 16%