Scores on a statistics exam are normally distributed with a

Scores on a statistics exam are normally distributed with a mean of 80. What is the probability of selecting a student from this class that received a score less than one and half standard deviations below the mean?

Solution

we know that this is normally distributed so

if we take values below the mean will be 0.50

if we take values above the mean will be 0.50

and we know that the data inside of miu + / - 1 standard deviation is 68%

so

probability of selecting a student from this class that received a socre less than 1 and half standard deviation below the mean will be 0.50 - 0.68 / 2 = 0.16

16%