Question

A coin is flipped 12 times. Using the normal approximation of the binomial distribution, calculate the probability of observing either 6, 7, or 8 heads.

Answer 1

Here by flipping a coin

• Probability of observing either heads or tails = 0.5
• here n =12 and r may be either 6, 7 and 8

By applying the binomial distribution formulas for mean and standard deviation we have the following as shown in the figure

Therefore at Z=1.15 ; looking at the normal distribution table the probability at this Z Value is 0.3749

Since the normal curve is symmetrical around the mean there is 50% data that lies below the mean and 50% above the mean. Therefore the probability of finding either 6, 7 or 8 heads will be 0.3749 = 37.49%