Question

a fair coin is flipped 44 times. let X be the number if heads. what normal distribution best approximates X?

Answer 1

n = Number of trials = 44

p = Probability of success = 0.5

q= Probability of failure = 1 - 0.5 = 0.5

Mean = np = 44 X 0.5 = 22

SD =

Conditions for Normal approximation to Binomial are satisfied as follows:

np = 40 X 0.5 = 22 >5

and

n(1- p) = 44 X (1 - 05) = 22> 5

So,

Normal distribution that best approximates X is as follows:

Normal Distribution with mean = = 22 and SD = = 3.3166