Question

From the past experience, a prof knows that the test score of a student taking his final xm is a random variable with mean 75 and variance 25.what os can be said about the probability that a student will score between 65 and 85.

Answer 1

Let X be the score of a student.

Then,

$P(65<X<85)=P(-10<X-75<10)=P(|X-75|<10)$

$=1-P(|X-75|\ge 10\ge 1-\frac {25} {100} =\frac 3 4=75$ %

So, the probability that a student will score between 65 and 85 is 75%