Statistics and Probability Answers

A. Construct a scatterplot of the following bivariate data:

1. 

Age of person, in years | 11 | 12 | 13 | 14 | 15 |

Weight (kg)          | 40 | 42 | 38 | 45 | 51 |   

2. 

Age of car, in years  | 11 | 12 | 13 | 14 | 15 | 

Mileage, in km/liter | 40 | 42 | 38 | 45 | 51 | 

B. Identify the dependent and independent variable in each of the following pairs of variables. Write your answer on the space provided

1. The base and the area of the triangle.

Independent Variable:

Dependent Variable:

2. Cost and age of car.

Independent Variable:

Dependent Variable:

3. The age and birth date.

Independent Variable:

Dependent Variable:

 In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses resulted in a mean of 96,700 miles and a standard deviation of 37,500 miles. At the 0.05 level of signıficance, test the manufacturer's claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

1. Claim:

Ho:

Ha:

2. Level of Significance:

Test- statistic:

Tails in Distribution:

3. Reject Ho if:

4. Compute for the value of the test statistics.

5. Make a decision:

6. State the conclusion in terms of the original problem.

Survey tests on seIf-concept and on leadership skill were administered to student-leaders. Both tests use a 10-point Likert scale with 10 indicating the highest scores for each test. Scores for students on the tests follow:

Student  | A |  B  |   C  | D  |   E  |   F  | G | 

Self-

Concept | 7.1 | 5.6 | 6.8 | 7.8 | 8.3 | 5.4 | 6.3 |

Leader  | 3.4 | 6.0 | 7.8 | 8.8 | 7.0 | 6.5 | 8.3 |

-ship Skill

1. Compute the coeficient of correlation r.

2. Interpret the results in terms of strength and direction of correlation.

3. Find the regression line that will predict the leadership skill if the self-concept score is known

Statistics and ProbabilityA secretary goes to work following one of three routes A, B, C. Her choice of route is independent of the weather. If it rains, the probabilities of arriving late, following A, B, C are 0.06, 0.15, 0.12 respectively. The corresponding probabilities, if it does not rain, are 0.05, 0.10, 0.15 respectively. Given that on a sunny day she arrives late, what is the probability that she took route C? Assume that on an average one in every four days is rainy.

In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

A well-known consulting firm wants to test how it can influence the proportion of questionnaires returns for its surveys. In the belief that the inclusion of an inducement to respond may be influential, the firm sends out 1000 questioners: 200 promise to send respondents a summary of the survey results; 300 indicate that 20 respondents (selected by a lottery) will be awarded gifts; and 500 are accompanied by no inducements. Of these, 80 questionnaires promising a summary, 100 questionnaires offering gifts, and 120 questionnaires offering no inducements are returned. What can you conclude from these results?

Two fair dice are thrown, one red and one blue. What is the

probability that the red die has a score that isstrictly greater

than the score of the blue die? Why is this probability

less than 0.5? What is the complement of this event?

A recent survey showed that 60 percent of the population own some kind of microcomputer and 40 percent do not. Market experts predict that in a year 10 percent of the non owners will become owners, and 1/100 of one percent of the owners will become nonowners.

What is the predicted steady state for the next year?

The scores on a national achievement exam are normally distributed with a mean of 600 and a standard deviation of 120. If a student is selected at random, find the probability that the student scored above 660

If an automobile gets an average of 27 miles per gallon on a trip and the standard deviation is 3 miles per gallon, find the probability that on a randomly selected trip, the automobile will get between 21 and 30 miles per gallon. Assume the variable is normally distributed.