MTH 4451 Test #1 Spring 2014

Transcription

1 Pat Rossi Instructions. MTH 4451 Test #1 Spring 2014 Name Show CLEARLY how you arrive at your answers. 1. A random sample of the ight times (in minutes) of ten nonstop ights from Atlanta to Los Angeles is given below: Compute the following: f301; 298; 300; 315; 297; 306; 292; 311; 306; 314g (a) mean (b) median (c) mode (d) range (e) variance (f) standard deviation (g) coe cient of variation (express this as a percentage by multiplying by 100%)

2 2. How many seven card hands can be drawn from a standard deck of 52 playing cards? 3. An accredited college Study Abroad program o ers US college students the following Study Abroad opportunity. From the group of countries Argentina, Australia, Brazil, China, Denmark, England, France, Germany, Japan, Korea, Morocco, New Zealand, Nigeria, Portugal, Spain, and Sweden (16 countries in all), a student can select four countries to study in - each country for a period of three months. Each three-month term corresponds roughly to a season of the year (Fall, Winter, Spring, and Summer), hence, studying in Australia during the Summer (June-July-August) would be di erent from studying in Australia during the Winter (December-January-February). How many di erent Study Abroad opportunities are possible in this program? 4. A bag contains 15 red balls, 10 green balls, 7 yellow balls, 5 blue balls, and 3 white balls. (a) What is the probability that a ball, selected at random, is red? (b) What is the probability that a ball, selected at random, is neither green nor white? 2

3 5. A pair of dice is tossed. (a) Draw the sample space. (b) Compute the probability of getting a 5. (c) Compute the probability of getting a 4 or an Suppose that P (A) = 0:38; P (B) = 0:81; and P (A \ B) = 0:25 (a) Compute P (A [ B) (b) Compute P (A c ) (c) Compute P (A c \ B c ) 3

4 registered voters are surveyed and the results are listed below: Republican Democrat Total Man Woman Total (a) Write the joint probability table. (b) Based on the marginal probabilities, if one voter is selected at random, compute: 1. The probability of the voter being Republican 2. The probability of the voter being Democrat (c) Based on the marginal probabilities, if one voter is selected at random, compute: 1. The probability of the voter being a man 2. The probability of the voter being a woman (d) What is the probability of selecting a voter that is both a man and a Democrat? (e) If the voter selected is a man, what is the probability that he is also a Democrat? (f) Is being a Democrat independent of being a man? Explain, using probabilities. 4

5 8. Marketers have found that 85% of Montgomery residents who have their cable TV supplied by Media Productions also have their internet service provided by Media Productions. Of all residents in Montgomery, 43% have their Cable TV service provided by Media productions. Finally, 42% of Montgomery residents have their internet service provided by Media Productions. Let T be the event that a Montgomery resident has their cable TV supplied by Media Productions Let I be the event that a Montgomery resident has their internet service provided by Media Productions. (a) What is the probability that a Montgomery resident, selected at random, has both their cable TV and their internet service provided by Media Productions? (b) What is the probability that a Montgomery resident, selected at random, does NOT has their cable TV supplied by Media Productions but DOES have their internet service provided by Media Productions? (c) Given that a Montgomery resident does NOT have cable TV provided by Media Productions, what is the probability that they DO have their internet service provided by Media Productions? 5

6 9. The mean height of adult American men is 70 inches with a standard deviation of 4 inches. (a) What percentage of the population of adult American men have heights between 62" and 78"? (b) What percentage have heights between 58" and 82"? (c) Use Tchebychev s Theorem to give an estimate of the percentage of adult American men whose heights are between 64" and 76." 6