Question

Answer ASAP

A fair coin is repeatedly and independently flipped for a total of 72 times and let X be the number of times a multiple of 3 is observed. Find the approximate probability of LaTeX: 15\le X<3215 ≤ X < 32 (be sure to apply all necessary adjustments to make your approximation as close to the true value as possible).

Answer 1

Probability that a toss of a fair coin results in an outcome which is multiple of 3 = 2/6 = 1/3

Average number of tosses out of 72 tosses in which a multiple of 3 is observed = 1/3*72 = 24

Standard deviation of number of tosses = $\sqrt{72*1/3*2/3}$ = 4

Let X be the number of tosses which results in multiple of 3

Since np = 24 and n(1 - p) = 48, X can be approximated to Normal distribution with Mean = 24, Standard deviation = 4

The required probability = P(15 ≤ X ≤ 32)

Using correction of continuity, the required probability = P(14.5 < X < 32.5)

= P{(14.5 - 24)/4 < Z < (32.5 - 24)/4}

= P( -2.375 < Z < 2.125)

= 0.9744