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MAT/STA 325 Exam 2 March 29, 2001 Prof. Thistleton
- A basketball player has b een practicing her foul shots and now can hit 60% of the time. Supp ose she attempts 14 shots. (Assume that the success of each of the shots is indep endent of the others).
What is the probability that she sho ots 6 of them successfully?
Compute this probability using the normal approximation to the binomial distribution.
- Supp ose that, out of a sample of 75 randomly selected individuals from a large p opulation, 25 are Demo crats. Calculate a 95% con dence interval for the prop ortion of Demo crats in the p opulation.
- Mark's do ctor is concerned that he may su er from hyp okalemia (low p otassium in the blo o d). There is variation in b oth the actual p otassium level in a p erson's blo o d from day to day and in the results from the blo o d test that measures this level. Mark's measured p otassium level varies according to the normal distribution with = 3 : 8 and = 0 :2. A patient is classi ed as hyp okalemic if his p otassium level is b elow 3.5.
If a single p otassium measurement is made, what is the probability that Mark is classi ed as hyp okalemic?
If a single p otassium measurement is made, what is the probability that Mark's p otassium level is b etween 3.7 and 3.9?
What is the probability that a sample of 35 measurements will have an average value greater than 3.9?
- You are trying to accurately measure the weight of a ro ck sp ecimen. You obtain the following measurements.
measurement A B C weight in grams 10.2 10.5 10.
Assume that the p opulation of measurements is normally distributed.
(a) Calculate the mean and standard deviation of the sample.
(b) Calculate the 90% con dence interval for the true weight of the sp ecimen.
(c) Calculate the 90% con dence interval for the standard deviation of the p opulation of all weights for the sp ecimen.
- Supp ose that a p opulation is normally distributed. You obtain a sample of size n = 10 from this p opulation and obtain a sample mean of 20.
(a) Calculate a 95% con dence interval for the p opulation mean if you know that the p op- ulation standard deviation is = 3.
(b) Calculate a 95% con dence interval for the p opulation mean if you do not know the p opulation standard deviation and must use the sample standard deviation s = 3.
- Supp ose again that a p opulation is normally distributed. Construct a 99% con dence interval for the p opulation standard deviation if, from a sample of size n = 30 you obtain s = 10 using
(a) the ^2 distribution.
(b) the large sample normal approximation.
