1. For the 16 teams in the National League data is shown for the team batting averages as of August 27, 2012. Determine the:

a) Mean

b) Median

c) Mode

d) Sample Standard Deviation

e) Coefficient of Variation

**Team** **Batting Average**

Arizona Diamondbacks .258

Atlanta Braves .253

Chicago Cubs .241

Cincinnati Reds .257

Colorado Rockies .269

Houston Astros .238

Los Angeles Dodgers .253

Miami Marlins .244

Milwaukee Brewers .252

New York Mets .253

Philadelphia Phillies .256

Pittsburgh Pirates .245

San Diego Padres .241

San Francisco Giants .265

St. Louis Cardinals .277

Washington Nationals .257

2. A study shows that of patients suffering from a certain disease, 72% die from the disease.

What is the probability that of 8 randomly selected patients:

a) 4 will survive the disease?

b) 2 or more will die from the disease?

c) Less than 2 will survive the disease?

3. A manufacturer of turbine blades finds that on the average, 12% of blades made are rejected because they are nonconforming. What is the probability that a batch of 10 blades will contain:

a) Less than 2 rejects?

b) 2 rejects?

4. Vehicles pass through a busy intersection at an average rate of 300 per hour.

a) Find the probability that none pass through the intersection in a given minute.

b) What is the expected number passing through in three minutes?

c) Find the probability that this expected number actually pass through in a given three-minute period

5. Twenty sheets of raw material are examined for surface flaws. The frequency of the number of sheets with a given number of nonconformances per sheet was as follows:

Number of flaws Frequency

0 4

1 3

2 5

3 2

4 4

5 1

6 1

What is the probability of finding a sheet chosen at random which contains 3 or more surface flaws?

6. Professor Kyle has 150 students in his college mathematics lecture class. The scores on the final exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 82 and 90?

7. A machine is used to fill bottles of water bottles. The amount of soda dispensed into each bottle varies slightly. Suppose the amount of soda dispensed into the bottles is normally distributed. If the average is 590 and at least 99% of the bottles must have between 585 and 595 milliliters of water, find the greatest standard deviation, to the *nearest hundredth,* that can be allowed.

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