For the following distribution function $F\left(x\right)$ of a random variable $X$

x	1	2	3	4	5	6
F(x)	0.2	0.37	0.48	0.62	0.85	1

$P \left(3<X \le 5\right)=$

• A

  $0.48$
• Correct answer
  B

  $0.37$
• C

  $0.27$
• D

  $1.47$

Solution

$P\left(3<x\le 5\right) =P\left(x=4\right)+P(x=5)$
$=\left(F\left(4\right)-F\left(3\right)\right)+\left(F\left(5\right)-F\left(4\right)\right)$
$=0.14+0.23$
$=0.37$

Hence, the correct answer is option: 'B'.