Home › MCQs › EEJ MAIN Mathematics › Question #6984
Back to Questions
EEJ MAIN Mathematics QUESTION #6984
Question 1

A bag has 30 white and 10 red balls. Balls are drawn one at a time with replacement, 16 times total. Let $X$ = number of white balls drawn. Find $\dfrac{\text{mean of }X}{\text{standard deviation of }X}$.

  • 4
  • $4\sqrt{3}$✔️
  • $3\sqrt{2}$
  • $\dfrac{4\sqrt{3}}{3}$
Correct Answer Explanation

$n=16$, $p=\dfrac{30}{40}=\dfrac{3}{4}$, $q=\dfrac{1}{4}$.

$\text{Mean} = np = 16\times\dfrac{3}{4} = 12$

$\text{Variance} = npq = 16\times\dfrac{3}{4}\times\dfrac{1}{4} = 3$

$\text{SD} = \sqrt{3}$

$\dfrac{\text{Mean}}{\text{SD}} = \dfrac{12}{\sqrt{3}} = \dfrac{12\sqrt{3}}{3} = 4\sqrt{3}$