# In a recent survey, 80% of the citizenry in a community favored the building of a municipal golf course

November 24, 2016

1. In a recent survey, 80% of the citizenry in a community favored the building of a municipal golf course. If you ask 15 citizens about this project, find the probability that

a. at least 9 favor the golf course project.
b. exactly 9 favor the golf course project.
c. less than 9 favor the golf course project.

2. The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. The distribution of mean response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes.

a. Find the probability that a randomly selected response time is less than 15 minutes.

b. Find the probability that a randomly selected response time is between 13 minutes and 15 minutes.

c. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be in order to qualify for the special safety award?

3. Parker Seal, Inc. makes O-rings for newly planned commercial space shuttles. The rings are designed to seal connections and joint fillings in the fuel system to prevent leaks. One type of ring should be 5 centimeters in diameter in order to fit properly. A sample of 49 of these type of O-rings is selected and the diameters are measured The sample results are as follows:

Sample Size = 49
Sample Mean = 5.05 centimeters.
Sample Standard Deviation = .14 centimeters.

a. Construct a 99% confidence interval for the average diameter of this type of O-Ring.

b. Interpret this interval.

c. How large a sample size will need to be selected if we wish to have a 99% confidence interval for the average diameter of this type of O-Ring with a margin for error of .02 centimeters?

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