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For the data in the spreadsheet assessment2.xls, calculate the:
1. mean:
30.6
33.1
40.2
128.2
2. median:
30.6
33.1
40.2
128.2
3. range:
30.6
33.1
40.2
128.2
4. standard deviation:
30.6
33.1
40.2
128.2
5. A manufacturer of electrical resisters has a 10 ohm. resistor that has a published specification that says the resistance will be in the range 9.8 to 10.2 ohms. A random sample of 1000 resistors is measured, with the mean value of the resistance being 10.06 ohm. with a standard deviation of 0.12 ohm. If we assume the resistance is distributed normally, what fraction of resistors will fail to meet the specifications?
1.5%
4.8%
12.2%
13.7%
6. A cybercafe wants to determine the average amount of time its customers spends cruising the web during a visit. After adding a simple login screen to their PCs, the company can measure the amount of time each customer is logged in. The following spreadsheet contains a random sample of login times for 100 customers from the past month:
A 99% confidence interval for the average login time for a cybercafe customer is:
11.01 +/- 1.72
11.01 +/- 2.05
11.01 +/- 2.43
11.01 +/- 2.69
7. A special variety of heart-healthy eggs claims to have a lower level of cholesterol than the average egg. The average grade A large egg has 250 mg. of cholesterol. A nutrition laboratory takes a random sample of 20 grade A large eggs, measures the amount of cholesterol and comes up with an average of 238.4 mg. with a standard deviation of 23.4. Test whether the mean level of cholesterol in the heart-healthy eggs is less than the average of 250 mg. What is the probability that the heart healthy eggs have an average of 250 mg. of cholesterol given the data in the sample, i.e. what is the p-value?
0.0045
0.0124
0.0195
0.0545
8. A prototype for a new parallel-processing computer is to be built using 20 prototype chips. The chip manufacturing process is very expensive, so the company does not want to make any more chips than it has to. In addition, the setup costs are such that all chips should be made in one batch to minimize manufacturing costs. Because the chip manufacturing process is new, 60% of the chips produced are defective. The R&D Manager has recommended that a batch of 50 processors should be produced, since (50)(0.4) = 20, so out of the 50 chips there should be 20 good ones to use in the prototype computer. If 50 chips are produced and there is a 60% chance that each chip will be defective, what is the probability that there will be enough chips to manufacture the prototype computer?
11.1%
44.6%
55.4%
88.9%
Hint: First solve for the probability that there will not be enough chips using the cumulative binomial probability function in Excel.
9. A candidate for mayor at a major city claims the prosecutors office is lax on crime and only prosecutes 30% of the criminal cases brought to it, choosing to either drop charges or plea-bargain the other 70%. To verify this claim, a local reporter uses the freedom of information act to request data from the files of 50 randomly selected individuals arrested by the police in the city the last year. Of the 50 arrested individuals, 21 were prosecuted. Does this data contradict the candidates claim? What is the probability that the candidates claim is still valid given the data in this sample, i.e. what is the p-value?
0.013
0.032
0.064
0.102
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