Table Lists - Probablity - Exam, Exams of Probability and Statistics

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FINAL EXAM REVIEW

Name___________________________________

1)The table lists the smoking habits of a group of college students.

Sex Non-smoker Regular Smoker Heavy Smoker Total Man 135 52 5 192 Woman 187 21 12 220 Total 322 73 17 412

If a student is chosen at random, find the probability of getting someone who is a regular or heavy smoker. Round your answer to three decimal places. Answer:0.

2)The distribution of Master's degrees conferred by a university is listed in the table. (assume that a student majors in only one subject)

Major Frequency Mathematics 230 English 208 Engineering 86 Business 176 Education 222

What is the probability that a randomly selected student with a Master's degree majored in English or Mathematics? Round your answer to three decimal places. Answer:0.

3)In the game of craps, two dice are tossed and the up faces are totaled. Is the event getting a total of 9 and one of the dice showing a 6 mutually exclusive? Answer Yes or No. Answer:No

4)The table lists the smoking habits of a group of college students.

Sex Non-smoker Regular Smoker Heavy Smoker Total Man 135 69 5 209 Woman 187 21 5 213 Total 322 90 10 422

If a student is chosen at random, find the probability of getting someone who is a woman or a heavy smoker. Round your answer to three decimal places. Answer:0.

5)If one card is drawn from a standard 52 card playing deck, determine the probability of getting a seven or a nine or a heart or a diamond. Answer:0.

6)You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 3.

Answer:^12 13

7)A game has three outcomes. The probability of a win is 0.4, the probability of tie is 0.5, and the probability of a loss is 0.1. What is the probability of not winning in a single play of the game. Answer:0.

8)A human gene carries a certain disease from the mother to the child with a probability rate of 47 %. That is, there is a 47 % chance that the child becomes infected with the disease. Suppose a female carrier of the gene hasfour children. Assume that the infections of thefourchildren are independent of one another. Find the probability that allfourof the children get the disease from their mother. Answer:0.

9)A human gene carries a certain disease from the mother to the child with a probability rate of 39 %. That is, there is a 39 % chance that the child becomes infected with the disease. Suppose a female carrier of the gene hasfive children. Assume that the infections of thefivechildren are independent of one another. Find the probability that at least one of the children get the disease from their mother. Answer:0.

10)In how many ways can a committee of three men and four women be formed from a group of 10 men and 10 women? Answer: 25200

11)How many distinct arrangements can be formed from all the letters of "statistics"?

Answer:50,

12)Given the sets of digits {1, 3, 4, 6, 8}, how many different numbers between 40,000 and 80,000 can be written using these digits if repetition of digits is allowed? Answer: 1250

13)Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last.

Answer:720; 24;^1 30

14)From 8 names on a ballot, a committee of 3 will be elected to attend a political national convention. How many different committees are possible? Answer: 56

15)The random variable x represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x.

x P(x) 0 0. 1 0. 2 0. 3 0. 4 0. Answer:mean: 1.18; standard deviation: 1.

28)Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of12.34ouncesand a standard deviation of 0.04 ounce. Find the probability that the bottle contains between12.24and12.30ounces. Answer:.

^

Professor Whata Guy surveyed of his Introduction to Statistics class of 420 students. One of the questions was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is the sample proportion, p? Answer:0.

30)Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completed that shift, what is the probability that he will find less than 20 substandard welds? Answer:0.

31)A survey of 500 non-fatal accidents showed that 222 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone. Answer:(0.387,0.501)

32)An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 513 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90 % confidence level. Answer:.37±.0 35

33)Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90 % confidence interval. Answer:.5625±.0 129

34)Construct a 90% confidence interval for the population mean,μ. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. Answer:(2.51, 3.21)

35)How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sampled results show that sample mean and standard deviation were$18.00 and$3.30, respectively. Use this information to create a 95 % confidence interval for the mean. Answer: 18 ±2.262(3.30/ 10 )

36)Construct a 95% confidence interval for the population mean,μ. Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2. Answer:(77.29, 85.71)

37)A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed.

$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.

Find the 95% confidence interval for the true mean. Answer:($3.39, $6.01)

38)The grade point averages for 10 randomly selected high school students are listed below. Assume the grade point averages are normally distributed.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.

Find a 98% confidence interval for the true mean. Answer:(1.55, 3.53)

39)Suppose you are using΅=0.05 to test the claim thatμJ 32 using a P-value. You are given the sample statistics

n=35,x=31.1,andΗ=2.7.Find the P-value. Answer:0.

40)GivenH 0 :μ=25,H 1 :μJ25, and P=0.028. Do you reject or fail to rejectH 0 at the 0.01 level of significance?

Answer:fail to rejectH 0

41)GivenH 0 :μL18,H 1 :μ<18, and P=0.068. Do you reject or fail to rejectH 0 at the 0.05 level of significance?

Answer:fail to rejectH 0

42)A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5. A random sample of 40 teachers provided the data below. At΅=0.05, test the district's claim using P-values.

0 3 6 3 3 5 4 1 3 5 7 3 1 2 3 3 2 4 1 6 2 5 2 8 3 1 2 5 4 1 1 1 21 5 7 5 4 9 3

Answer:P-value=0.000001, P<΅, rejectH 0 ; There is sufficient evidence to support the school district's claim.

48)Given a sample with r=-0.765, n=22, and΅=0.02, determine the standardized test statistic t necessary to test the claimΕ=0. Round answers to three decimal places. Answer:-5.

49)For the data below, test the significance of the correlation coefficient using΅=0.10 and the claimΕ=0.

x y

Answer:critical valuet 0 =±1.860; standardized test statistic tY0.296; fail to rejectH 0 ; There is not sufficient evidence to conclude that a significant correlation exists.

50)Given a sample with r=-0.541, n=20, and΅=0.01, determine the critical valuest 0 necessary to test the claim

Ε=0. Answer:±2.

51)Find the equation of the regression line for the given data.

x y

Answer:

^ y=2.097x-0.

52)The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Find the equation of the regression line for the given data.

Gestation, x 8 2.1 1.3 1 11.5 5.3 3.8 24. Life span, y 30 12 6 3 25 12 10 40

Answer:

^ y=1.523x+6.

53)A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data.

Miles traveled, x Sales, y

Answer:

^ y=3.529x+37.

Given the equation of a regression line is^y=3.5x-5.4, what is the best predicted value for y givenx=-1.2? Assume that the variables x and y have a significant correlation. Answer:-9.

55)Given the equation of a regression line is^y=-4.5x-3.4, what is the best predicted value for y givenx=9.5? Assume that the variables x and y have a significant correlation. Answer:-46.

use alpha .05 the given data to find the best predicted value of the response variable.

^

The regression equation relating dexterity scores (x) and productivity scores (y) for the employees of a company isy=5.50+1.91x.Ten pairs of data were used to obtain the equation. The same data yieldr=0.986andy=56.3. What is the best predicted productivity score for a person whose dexterity score is 32? Answer:66.

^ Six pairs of data yield r=0.444 and the regression equationy=5x+ 2 .Also,y=18.3.What is the best predicted value of y forx= 5? Answer:18.

^ Nine pairs of data yield r=0.867 and the regression equationy=19.4+0.93x.Also,y=64.7.What is the best predicted value of y forx= 50? Answer:65.

Answer Key

Testname: FINAL_EXAM_REVIEW

There appears to be no linear correlation. 44)0. 45)0. 46)0. 47)-2. 48)-5. 49)critical valuet 0 =±1.860; standardized test statistic tY0.296; fail to rejectH 0 ; There is not sufficient evidence to conclude that a significant correlation exists. 50)±2. 51)y^=2.097x-0.

^ y=1.523x+6.

y^=3.529x+37. 54)-9. 55)-46. 56)66. 57)18. 58)65.