Normal Approximation to Binomial Distribution

A fair coin is tossed 16 times. Let X be the total number of heads. Then X is a binomial random variable with mean 8 and standard deviation 2. We have P(X=3)=0.009; P(X=4)=0.028; P(X=5)=0.067; P(X=6)=0.122; P(X=7)=0.175; P(X=8)=0.196; P(X=9)=0.175; P(X=10)=0.122; P(X=11)=0.067; P(X=12)=0.028. The binomial distribution can be approximated by the normal distribution with mean 8 and deviation 2. For example, P(6<=X<=9)=0.668. The area under the normal curve is 67%.