An IQ test has a mean of 100 and standard deviation of 15. What percentile does 114 and 140 lie in and what is the score is needed to be in he 99th percentile?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The percentile of a value chosen from a set of observations is the percentage of observations that fall below the chosen value.

In the IQ test, the mean is 100 and the standard deviation 15.

To determine the percentile that a score 114 is in, find the z-score of 114. This is equal to (114 - 100)/15 = 0.9333. Using a normal table, the value for 0.933 is 0.8238. 114 is in the 82.38th percentile. For 140, the z-score is 2.67. The value for 2.67 from a normal distribution table is 0.9962. 140 lies in the 99.62th percentile.

From the normal distribution table, the z-score corresponding to 99% is 2.41. The score corresponding to this is 136.15

The percentile a person with a score of 114 is in is 82.38. A score of 140 lies in the 99.62th percentile and the minimum score that lies in the 99th percentile is 136.15

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial