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Practice+Test+5A-Solutions - Practice Test 5A 1 A die...

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Unformatted text preview: Practice Test 5A 1. A die is rolled five times. What is the probability of getting exactly three “ones?” a. .03215  ­ ­ ­use the BD Formula (the WHOLE thing) 2. As N increases, what happens to the skew of the distribution of the binomial distribution? Explain why this is true. a. Becomes more normal. This it becomes closer to zero. As N increases the denominator increases this skew goes to zero. 3. There are three red balls, a blue ball, two yellow balls, and four green balls. What is the total number of combination possible? a. 12600 (use first part of BD) 4. There is a quiz of 192 multiple ­choice questions. There are four choices. Bob will fail the class if he doesn’t get more than 60 correct on the test. Unfortunately for Bob, he hasn’t studied at all and will be merely guessing. What is the probability that Bob will be failing the class? Please feel free to treat the distribution as if it were continuous. In fact, is it encouraged. a. EV=48; SD = 6 calculate z ­score to get .9772 5. You take your kid brother to a candy shop. There are seven types of gummies, five types of gumdrops, three types of licorice, six types of chocolate, and four types of taffy. You let him pick two of each. How many variations are there? a. 56700 (use BD for each type of candy. Use first half) 6. You flip a coin 2500 times. What is the probability of getting between 1260 and 1280 tails? Please feel free to treat the distribution as if it were continuous. Its encouraged. a. EV= 1250 SD=25 Use Z ­score to get .2295 7. Your friend takes a true and false test where there are five questions. What is the probability of getting exactly four or more correct (if you are completely guessing). Do not treat this as if it were continuous. Treat it as the discrete distribution it is. a. Use entire BD formula to get .1875. Remember to do TWO BD because you want 4 and great than 4. (Similar to example we did in LARC about the salesman and insurance). 8. Your friend Adam has a padlock and forgot how to open it. There are four dials, and each contains the digits 0 ­9. He says that’s okay; he’ll just try every possible way to order the numbers. How many possible ways are there? a. 10x10x10x10= 10000 9. There is a probability for a random variable X. X is the number of “ones” you get when you roll a die five times. What is the skew of this probability distribution? a. (1 ­2MU)/√nMUq= (1 ­2(1/6))/√5x1/6x 5/6= .8 10. There is group of six freshman, five sophomores, and eight juniors. How many ways can a committee of six be formed if it must consist of two from each of the three class levels (two freshman, two sophomores, and two juniors)? Please calculate the answer. You may leave it in fractional form if you wish. a. First half of BD for each class level. Answer ­4200 11. A certain portfolio consists of eight stocks. The investor feels that the probability of any one stock going down in price is .40 and that the price movements of stocks are independent. What is the probability that exactly five stocks will decline? You must show your work. a. N=8 p=.4 k=5 thus you get .12386 12. As N increases, what happens to the kurtosis of the binomial distribution? a. Becomes more mesokurtic or approaches 3. 13. A spinner comes up “blue” one fourth of the time. What is the probability of getting between 189 and 210 “blues”? You must show work. a. N=768 ev=193 and SD=12 Calculate z ­score for 189 and 210. Z ­scores equal  ­.25 and 1.5 respectively and you get .010989 and .5319. 14. The probability of having a TV is .98. George wants to look at the binomial distribution for number of homes with TVs for a sample of a particular size. He wants to be able to use a normal approximation, however. Thus, how large does his sample have to be in order to use the normal approximation? a. .98 x N > 5 and .02 x N > 5 – N > /.02= 250 15. The arrival of a bird on a remote island is independent from the arrival of another bird on the island. On average, over the period of a week, six birds arrive on the island. What is the probability of exactly four birds arriving? Show work. a. E^ ­6 * 6^4/4!= .0024787 (1296/24)= .13385 16. A test has a mean of 250 and a SD of 25. What is the probability of picking someone at random who has a score between 210 and 240? Show work. a. Use z0score formula for both 210 and 240. You get  ­1.6 and  ­0.4 respectively. .4452 ­.1554= .2898 17. I want to know what the probability of getting exactly 3 hearts if I am dealt 10 cards. Can I use the binomial distribution to figure this out? Explain why or why not. a. No. The events aren’t independent. 18. When is the Poisson distribution a good approximation for the binomial distribution? a. When P is very small for a given interval and N is very large. ...
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