Reference no: EM13584229

1. If the random variable z is the standard normal score and P(z < a) > 0.5, then a > 0.  Why or why not?

2. Given a binomial distribution with n = 27 and p = 0.81, would the normal distribution provide a reasonable approximation?  Why or why not?

3. Find the area under the standard normal curve for the following:

(A) P(z < -1.13)

(B) P(0 < z < 1.29)

(C) P(-0.89 < z < 0.91)

4. Find the value of z such that approximately 27.64% of the distribution lies between it and the mean.

5. Assume that the average annual salary for a worker in the United States is $33,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following:
 
(A)  What percentage of Americans earn below $21,000?
(B)  What percentage of Americans earn above $41,000?
 
Please show all of your work.

6. X has a normal distribution with a mean of 80.0 and a standard deviation of 4.0. Find the following probabilities:

(A) P(x < 75.0)

(B) P(75.0 < x < 85.0)

(C) P(x > 87.0) (Points : 6)

7. Answer the following:

(A) Find the binomial probability P(x = 4), where n = 14 and p = 0.60.

(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.

(C) How would you find the normal approximation to the binomial probability P(x = 4) 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.