A group of students with normally distributed salaries earn an average of $6,800 with a standard deviation of $2,500. What proportion of students earn between $6,500 and $7,300?
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A group of students with normally distributed salaries earn an average of $6,800 with a standard deviation of $2,500. What proportion of students earn between $6,500 and $7,300?
Let
be a normally distributed random variable with mean, 
, and standard deviation, 
. The probability that 
is between 
and 
is the area under the standard normal curve given by 
Here, given that average,
and 
, we have 
Therefore, the proportion of students that earn between $6,500 and $7,300 is 0.12702 or 12.7%.