An intersesting application of the normal distribution is that it can be utilized to approximate a binomial distribution. For example, lets say an unfair coin is knwon to have a probability of flipping heads 70% of the time (P=.70). If you decide to flip a coin 25 times, what is the probability that you get heads 18 or fewer times?
Since a normal distibution is defined completely using the expected value and standard deviation...
1) find the expected value and standard deviation of the binomial distribution
Using these values will provide us with a normal distribution that will approximate the underlying binomial distribution. Since the are under the curve represents the probability, we can find the area under of the normal distribution that directly corresponds to the probability of getting 18 or fewer heads.
2) Find the P(X<18.5). (you should convert your values before using the Z-chart)
Please answer both questions, thanks