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# Stats

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1. The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41, and 22. What are the population mean, variance, and standard deviation?

2. The weights of a sample of seven FedEx shipments, to the nearest pound, are 10, 7, 11, 10, 13, 5, and 4. Compute the sample mean, the median, and the modal weight.

3. The following is the number of shares traded (in 1,000's) for a sample of eight stocks listed on the New York Stock Exchange; 62, 41, 60, 49, 39, 45, 26, and 38. Compute the mean, range, and standard deviation.

4. An evaluation was undertaken to evaluate the mathematical ability of staff with an interest in economics. The results were as follows:

Ability in Mathematics
Interest in Finance Low Average High Total
Low 60 15 15 90
Average 15 45 10 70
High 5 10 25 40
Total 80 70 50 200

If a staff member is selected at random what is the probability that he or she
a. has a high ability in mathematics?
b. has an average interest in finance?
c. has a low ability in mathematics?
d. has a high interest in finance?
e. has a low interest in finance and a low ability in mathematics?
f. has a high interest in finance and a high ability in mathematics?
g. has a low interest in finance or a low ability in mathematics?
h. has a high interest in finance or a high ability in mathematics?
i. has a low ability in mathematics or an average ability in mathematics or a high ability in mathematics? Are these events mutually exclusive? Are they collectively exhaustive? Explain

5. Suppose, on a weekly basis, the lottery collects an average of 10.0 million dollars with a standard deviation of 2.5 million dollars. It is assumed that the distribution of the weekly collections follows a normal distribution. What is the probability that in any given week the collections will be

1. between 10.0 and 12.5 million dollars?
2. between 7.5 and 10.0 million dollars?
3. between 7.5 and 12.5 million dollars?
4. at least 7.5 million dollars?
5. under or less than 7.5 million dollars?
6. between 12.5 and 14.3 million dollars?
7. 50% of the time weekly collections are expected to be above what value?
8. 90% of the time weekly collections are expected to be above what value?

6. A building contractor claims he can renovate a 300 square foot kitchen and dining room in 40 work hours plus or minus 5 hours (i.e. The mean and standard deviation respectively). There are many elements to the project, like plumbing, electrical, installation of new appliances, etc. Assuming from past experience that times to complete similar projects are normally distributed with mean and standard deviation as estimated above;
1. What is the likelihood the project will be completed in less than 35 hours?
2. What is the likelihood the project will be completed in between 35 and 48 ours?
3. 10% of such projects require more than how many hours?

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