Q) An unbiased dice is thrown once. Write down the probability distribution of the score $X$ and show that $Var(X) = 35/12$
(Completed: $ \mu = 7/2, \sigma^2 = 35/12$ )
The same dice is thrown 70 times:
I: Find the probability that the mean score is less than 3.3
$P(X \le 3.3) $
$Z = X-\mu/\sigma$
$\implies Z = 7/2 - 3.3/\sqrt(35/12)$
$\implies Z=0.117$
$\implies Ans = \phi(0.117)$
$\implies = 0.5464$
(Correct Answer = 0.155)
II) Find the probability that the total score exceeds 260.
$ 260/70 = 3.714$
$\implies P(\bar {X}\ge 3.714285)$
$\implies 1-\phi(X-\mu/\sigma)$
$\implies 1-\phi(0.414285/1.707825128)$
$\implies 1-\phi(0.242580457)$
$\implies 1-0.5960$
$\implies = 0.404$
(Correct Answer: 0.139)