Q5Single correct3 Marks13 Jul 2025

Let $X$ be the number of items produced by a machine on a given day with $E[X]=7$ and $E[X^2]=55$. Using Chebyshev's inequality, find a lower bound on the probability that a machine produces between $4$ and $10$ items on a given day.

A

$\frac{2}{3}$

B

$\frac{1}{3}$

C

$\frac{1}{2}$

D

$\frac{3}{4}$