A certain standardized test has scores with a normal distrib

A certain standardized test has scores with a normal distribution having a Mean (\\mu ) of 30 and a Standard Deviation (\\sigma ) of 4. Several prospective test takers want to know what score they need to get so that they fall within a certain predetermined percentile. Assume all scores on this exam only take integer values. Therefore all scores should be rounded to the nearest integer. What score does a student need to get such that 33% of the students scored below?

Solution

the area between 1.0 standard deviation is about 67%

Area between 2 standard deviations is about 95%

In our case ,we require 67% confidence interval.Hence ,require area between 1 standard deviation.

which will be 30-4 to 30+4   -> hence the answer is 26 to 34.