Subject Mathematics Advanced Statistics

Question

4)
On a physical fitness test middle school boys are awarded one point for each push-up they can do, and a point for each sit-up. National results show that the expected value is 18 pushups with a standard deviation of 4 push-ups, and an expected value of 34 sit-ups with standard deviation 11 sit-ups. The expected value of their combined (total) scores is therefore 18 + 34 = 52 points. If the number of push-ups and the number of sit-ups are independent, what is the standard deviation of their combined scores?
A) 11.7 B) 15 C) 5.3 D) 7.2 E) 137

14)
One of the leading dot-com companies has found that the proportion of customers who come into its web site that actually makes a purchase is 0.045. After changing the design of the web site the company checks whether the 0.045 purchase rate still holds by selecting a random sample of 200 hits on their Web site. Given that the 0.045 rate still applies, what is the standard deviation of the sampling distribution of the sample proportion?
A) About 0.0002 B) About 0.0354 C) Approximately 0.0147 D) Can't be determined since the shape of the population distribution is not known.

16)
A printing company guarantees that no more than 5% of pages that it prints for textbooks have any type of printing error. Suppose that the printing company selects a random sample of 400 recently printed pages and finds 33 (8.25%) that have an error. If the printer is meeting the 5% standard, what is the probability that 8.25% or more of the pages in a sample of 400 pages would have errors ?
A) 0.1245 B) 0.4986 C) 0.0014 D) 0.1250

24)
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?
A) 398.8 sec B) 384.2 sec C) 515.8 sec D) 501.2 sec

25)
The sampling distribution of the sample mean is shown. If the sample size is n = 9, what is the standard deviation of the population from which the sample was drawn? Round to the nearest thousandth where appropriate.
A) Η = 13.333 B) Η = 4.444 C) Η = 120 D) Η = 360
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4)
σx 4
σy 11
σ(x+y) 11.7...

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