DOC PREVIEW
PSU STAT 401 - STUDY NOTES

This preview shows page 1-2 out of 5 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

STATISTICS 401: PRACTICE PROBLEMS FOR FINAL EXAMSpring 20001. The probability that an American engineering firm will establish a branch office in Torontois .7, the probability that it will establish a branch office in Mexico City is .4 and theprobability it will establish a branch office in at least one of the cities is .8. Define eventsA and B as follows:A = {American engineering firm will establish a branch office in Toronto}B = {American engineering firm will establish a branch office in Mexico City}It may be useful to draw Venn diagrams. For parts (a)-(c), what is the probability thata branch office will be established in(a) in both cities?(b) neither of the cities?(c) exactly one of the cities?(d) Are events A and B independent? Why or why not?2. From a load of 50 Panasonic Tape recorders 35 are destined for New York and 15 forBoston. If two are shipped to Trenton by mistake and the “selection” is random, whatare the probabilities thata) both tape recorders should have gone to New York;b) one should have gone to New York and one to Boston.3. From 5 biologists, 4 chemists, and 3 physicists,(a) how many committees of size 4 can be formed?(b) how many committees containing 2 biologists, 1 chemist, and 1 physicist can beformed?4. Seventy percent of the light aircraft that disappear while in flight in a certain countryare subsequently discovered. Of the aircraft that are discovered, 60% have an emergencylocator, whereas 90% of the aircraft not discovered do not have such a locator. Defineevents A and B as follows:A = {light aircraft that disappears is discovered}B = {light aircraft that disappears has an emergency locator}Suppose a light aircraft has disappeared.(a) What is the probability that it has an emergency locator and it will not be discov-ered?(b) What is the probability that it has an emergency locator?(c) If it has an emergency locator, what is the probability that it will not be discovered?5. Grafting, the uniting of the stem of one plant with the stem or root of another, is widelyused commercially to grow the stem of one variety that produces fine fruit on the rootsystem of another variety with a hardy root system. For example, most sweet orangesgrow on trees grafted to the root of a sour orange variety. Suppose that each graft failsindependently with probability .3.a) Write the formula for the p.m.f. for X, the number of grafts that fail in a series of fivetrials.b) Plot the cumulative distribution function F .c) Suppose that the cost of each failed graft is $9.00. Find(i) the probability that the cost from failed grafts will exceed $20.00 in the five trials.(ii) the expected cost from failed grafts in the five trials.(iii) the variance of the cost from the failed grafts in the five trials.6. Let X denote the amount of time for which the Stat 401 book on two-hour reserve atMcAllister is checked out by a randomly selected student, and suppose that X has densityfunctionf(x) =(.5x 0 ≤ x ≤ 20 otherwiseWhat is the probability that the book is checked out between .5 and 1.5 hours?7. The finished inside diameter of a piston ring is normally distributed with a mean of 10cm and a standard deviation of 0.03 c m.(a) Above what value of inside diameter will 85.08% of the piston rings fall?(b) What is the probability that the diameter of a randomly selected piston will be lessthan 10.06?8. Suppose your waiting time for the bus in the morning has mean 3 minutes and variance2825minutes, while the waiting time in the evening has mean 6 minutes and variance 4. Ina typical week, you take the bus 5 times in the morning and 3 times in the evening.(a) Calculate the expected value of the total waiting time in a typical week.(b) Calculate the variance of the total waiting time in a typical week. State your assump-tions.Hint: Set Xi= ith morning waiting time where i=1,...,5 and Yj= jth evening waitingtime where j=1,2,3.9. A question relating to a study of the echo-location system for bats is how far apart arethe bat and an insect when the bat first senses the insect. The technical problems formeasuring this are complex and so only 11 data points, Y1, . . . , Y11, were obtained. It isgiven that y = 48.36 and s2= 327.05.(a) Construct a 95% confidence interval for the mean distance µ.(b) What assumption did you use?10. An appliance manufacturer is considering the purchase of a new machine for cuttingsheet metal parts. If µ0is the average number of metal parts cut per hour by her oldmachine and µ is the corresponding average for the new machine, the manufacturer wantsto test the null hypothesis H0: µ = µ0against a suitable alternative. What should thealternative be if(a) she does not want to buy the new machine unless there is evidence it is more productivethan the old one;(b) she wants to buy the new machine (which has some other nice features) unless thereis evidence it is less productive than the old one?(c) For each of the two cases above s tate whether she should buy the new machine if thenull hypothesis gets rej ected.(d) Suppose that µ0= 9.5 cuts per hour and she decides to test H0: µ = 9.5 againstHa: µ > 9.5 at the α = .05 level. She gets the machine manufacturer to lend her anew machine and she measures the number of cuts made by the machine in fifty (50)randomly selected one hour time p eriods. The summary statistics for this random samplearex = 9.8 and s = 1.095. Would you reject H0?11. A study of the electromechanical protection devices used in electrical power systemsshowed that of 193 devices that failed when tested 75 where due to mechanical partsfailures.(a) Find a 95% confidence interval for p, the proportion of failures due to mechanicalcauses.(b) How large a sample is required to estimate p within 0.03, i.e. to have a confidenceinterval of length 0.06, with 95% confidence;(i) when you have no idea of what p might be;(ii) when a preliminary study investigations leads you to believe that p ≈ .3912. A manufacturer of automatic washers provides a particular model in one of three colors,white, almond, or blue. Of the first 1000 washers sold, it is noted that 400 of the washerswere white The manufacturer wants to know if this is evidence that more than a third ofconsumers prefer white washers.(a) Set up the appropriate null and alternative hypotheses for the manufacturer.(b) Carry out a test of your null hypothesis versus your alternative hypothesis at theα = .05 level. Is there evidence that more than one third of consumers prefer whitewashers?(c) What is


View Full Document
Download STUDY NOTES
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view STUDY NOTES and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view STUDY NOTES 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?