Question: Using normal distribution of the random variable X as an approximation of the binomial distribution, with parameters N=50 and P=2/3.
a. Calculate the mean and standard deviation of X.
b. By using this normal approximation, calculate P(30<X < 40)
c. If you perform this experiment nine times and calculate the average of the nine experiments \(\bar{X}\), calculate \(\Pr \left( 30<\bar{X}<40 \right)\)