Question

Use the normal distribution to approximate the desired probability. Find the probability that inA) 194 tosses of a fair die, we will obtain at least 36 twos. B) 27.29133% 27.09133% C) D) 26.79133% 27.64133% E) F) 27.34133% 26.89133% G) None of These

Answer 1

The normal distribution can be used as an approximation to the binomial distribution, under certain circumstances, namely:

• If X ~ B(n, p) and if n is large and/or p is close to ½, then X is approximately N(np, npq)

Here probability of two (or any face) in a fair dice = 1/6

So here, mean = np = 194/6 = 32.33

variance = 194 * (1/6) * (5/6) = 26.94

standard deviation = 5.19

Desired probability,

$P(X > 36) = 1 - P(X < 36) = 1 - P(\frac{X - 32.33}{5.19} < \frac{36 - 32.33}{5.19})$

$= 1 - P(Z < 0.707)$

= 1 - 0.76115

= 0.23885 (23. 885%)

So Option G is correct.

** If your answer does not match please comment.