Question

A coin with two sides, heads and tails, is flipped 100 times. What is the probability that a "heads" will come up exactly 60 times?

Submit your answer as a decimal fraction (range:  0 to 1) to five (5) decimal places.

Answer 1

Answer)

N = 100

P = 0.5 (as probability of getting heads is = 0.5)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 50

N*(1-p) = 50

Both the conditions are met so we can use standard normal z table to estimate the probability

P(exactly 60 = p(59.5<x<60.5) = p(x<60.5) - p(x<59.5)

P(x<60.5)

Mean = n*p = 50

S.d = √{n*p*(1-p)) = 5

Z = (x - mean)/s.d

Z = (60.5 - 50)/5 = 2.1

From z table, P(z<2.1) = 0.9821

P(x<59.5)

Z = (59.5 - 50)/5 = 1.9

From z table, P(z<1.9) = 0.9713

Probability = 0.9821 - 0.9713 = 0.0108