The approximate percentage of values in a data set that will fall between the 18

Question

The approximate percentage of values in a data set that will fall between the 18th percentile and the 39th percentile is:

The answer is 21% but I don't know how to get that

There are 350 statistic students at a Community College who have a mean grade point average of x = 2.8 and a standard deviation of s = 0.6. Which of the following grade point averages would be an“unusual” grade for statistic students at MCC? Consider a value unusual if it is not within 2 standard deviations of the mean.

Answer is 1.5 but don't know how to get that

Explanation / Answer

1. Percentile represents the % of data that is less than or equal to that value. So,

39 percentile means 39% of the data is less than or equal to that value and 18 percentile means 18% of the data is less than or equal to that value. So,

Data set that will fall between 18th and 39th percentile = 39% - 21% = 18%

2. Lowest cutoff value for 2 standard deviation from the mean = 2.8 - 2(0.6) = 2.8 - 1.2 = 1.6

Since 1.5 is below that lowest cutoff value. it will not be in the range of usual values.

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