This is an exercise in calculating the probabilities. You are given the Z values and one of the probabilities. Remember, 100% of data is under the curve. Answer the probability questions and fill in the blocks. Do not use the Tables or Empirical Rule. Calculate from information given. Z 1. P(Z>1.15) = 2. P(Z<1.15) = 3. P(-1.15 ____)

2. USE THE Z TABLES; DO NOT USE THE EMPIRICAL RULE. a) What are the Z scores for the middle 68%? b) What are the Z scores for the middle 95%? c) What are the Z scores for the middle 99.7%?

d) Calculate the probability between -1 standard deviation and 1 standard deviation. e) Calculate the probability between -2 standard deviations and 2 standard deviations. f) Calculate the probability between -3 standard deviations and 3 standard deviations.

3. The funds dispensed at the ATM machine follow a normal probability distribution with a mean of $3,800 per day and a standard deviation of $770 per day. The machine is programmed to notify the nearby bank if the amount dispensed is very low (less than $1,600) or very high (more than $5,850). (Hint: keep track of your variables and SKETCH it!)

a. What percent of the days will the bank be notified because the amount dispensed is very low?

b. What percent of the time will the bank be notified because the amount dispensed is very high?

c. What percent of the time will the bank not be notified regarding the amount of funds dispensed? (Hint: between the very low and very high)

4. A manufacturer of pipe had their quality-control department sample 600 ten-foot lengths. At a point 1 foot from the end of the pipe they measured the outside diameter. The mean of this diameter was 14 inches, and the standard deviation was 0.1 inches.

a. Using Chebyshev's Theorem, at least what percentage of the observations of the outside diameter will be between 13.85 and 14.15 inches? b. Using Chebyshev's Theorem, at least what percentage of the observations of the outside diameter will be between + - 3 standard deviations from the mean?

5. The salaries for the managers in a manufacturing plant are normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the managers who are in the top 2.5% of the salary schedule will not get a raise.

What is the salary level that divides the managers into one group that gets a raise and the group that does not?

6. A weight-loss program claims that the average weight people lose during the first two weeks of the program is 5.0 pounds. Assume the weight loss follows the normal distribution with a standard deviation of 3.0 pounds.

a. What is the probability that a person on the program will lose less than 7.0 pounds during the first two weeks?

b. What is the probability that a person will lose between 1.0 and 4.0 pounds during the