Set up, without solving, the binomial probability P(x is at most 5) using probability notation ...

1.Answer the following: (A) Find the binomial probability P(x = 5), where n = 13 and p = 0.50. (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. (C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. 

2. X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities: (A) P(x < 77.0) (B) P(78.0 < x 85.0) (C) P(x > 90)

3.Given a binomial distribution with n = 30 and p = 0.17, would the normal distribution provide a reasonable approximation? Why or why not? 

4. Find the area under the standard normal curve for the following: (A) P(z < -1.75) (B) P(0 < z < 0.14) (C) P(-0.51 < z a) > 0.5, then a > 0. Why or why not?

5. Find the value of z such that approximately 48.46% of the distribution lies between it and the mean