For any data set of n values with standard deviation s, every value must be within $s \sqrt { n - 1 }$ of the mean. In a class of 17 students, the heights of the students have a mean of 67.3 inches and a standard deviation of 3.2 inches. The tallest student in class, a hopeful member of the basketball team, claims to be
79.3 inches tall. Could he be telling the truth?

A) Yes
B) No

Question

For any data set of n values with standard deviation s, every value must be within $s \sqrt { n - 1 }$ of the mean. In a class of 17 students, the heights of the students have a mean of 67.3 inches and a standard deviation of 3.2 inches. The tallest student in class, a hopeful member of the basketball team, claims to be 
79.3 inches tall. Could he be telling the truth?

A) Yes
B) No

Quizplus · Accepted Answer

The tallest student's height is 79.3 inches, which is 12 inches (79.3 - 67.3) above the mean. The standard deviation multiplied by the square root of n - 1 is 3.2 * sqrt(17 - 1) = 12.8. Since 12 is less than 12.8, the student's claim is possible.

For Any Data Set of N Values with Standard Deviation sn−1s \sqrt { n - 1 }sn−1​

For Any Data Set of N Values with Standard Deviation $s \sqrt { n - 1 }$