Question

Suppose a fair coin (P[heads] = ½) is flipped 50 times. What is the probability of obtaining 30 or fewer heads using the normal approximation to the binomial with the continuity correction factor?

Use Minitab or some other software package to obtain the your probability answer. Round your answer to two decimal points.

Answer 1

Let X is a random variable shows the number of heads out of 50. Here X has binomial distribution with parameter n=50 and p=1/2 = 0.50.

Since np = 25 and n(1-p) = 25 both are greater than 5 so we can use normal approximation here.

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

Using continuity correction factor we have

The z-score for X = 30.5 is

The probability of obtaining 30 or fewer heads using the normal approximation to the binomial with the continuity correction factor is

Excel function used: "=NORMSDIST(1.56)"

Answer: 0.94