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.