Exam 2 MATH 1680

Suppose that events E and F are independent, P(E) = 0.8 and P(F) = 0.9. What is P(E and F)?

A) 0.72

Determine R^2 given that the linear correlation coefficient is -0.11.

A) R^2 = 1.21%

An instructor wishes to determine if there is a relationship between the number of absences from his class and a student's final grade in the course. What is the predictor variable?

A) absences

The number of violent crimes committed in a day possesses a distribution with a mean of 1.8 crimes per day and a standard deviation of four crimes per day. A random sample of 80 days was observed, and the sample mean number of crimes for the sample was calculated. The data that was collected in this experiment could be measured with a ___ random variable.

A) discrete

A contingency table relates

A) two categories of data

The probability that a football game will go into overtime is 15%. What is the probability that two of three football games will go into overtime?

B) 0.057

A help desk receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly six calls. Use the Poisson distribution.

B) 0.1042

Suppose that E and F are two events and that P(E and F) = 0.48 and P(E) = 0.5. What is (P|E)?

B) 0.96

In how many ways can a committee of three men and four women be formed from a group of 12 men and 12 women?

B) 108, 900

A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is a picture card.

B) 3/13

There are 36 chocolates in a box, all identically shaped. There are 6 filled with nuts, 14 with caramel, and 16 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.

B) 4/21

Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model, ^y= b.+b1x . Using the method of least squares, the faculty group obtained the following prediction equation, ^y=14,000 = 2,000x. Intercept the estimated slope of the line.

B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $2,000.

A researcher determines that the linear correlation is 0.85 for a paired data set. This indicates that there is

B) a strong positive linear correlation

If the two events have no outcomes in common they are said to be

B) disjoint

An unusual event is an event that has a

B) low probability of occurence

To eliminate the effects of either the row or the column variables in a contingency table, a _____ distribution is created.

B) marginal

The least squares regression line

B) minimizes the sum of the residuals squared

A manufacturer receives a shipment of 170 laptop computers of which 11 are defective. To test the shipment, the quality control engineer randomly selects 20 computers from the shipment and tests them. The random variable X represents the number of defective computers in the sample. What is the probability of obtaining 3 defective computers?

C) 0.0971

If one card is drawn from a standard 52 playing card deck, determine the probability of getting a ten, king, or a diamond. Round to the nearest hundredth.

C) 0.37

A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 15 members and any member can be elected to each position? No person can hold more than one office.

C) 2,730

A person can order a new car with a choice of 8 possible colors, with or without air conditioning, with or without heated seats, with or without anti-lock brakes, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered in terms of these options?

C) 256

Suppose x is a random variable for which a Poisson probability distribution with (*) = 8.7 provides a good characterization. Find (mu) for x.

C) 8.7

Calculate the mean for the discrete probability distribution shown here.

C) 8.93

Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment?

C) P(A) = 0, P(B) = 1/4, P(C) = 3/4

A recent survey found that 69% of all adults over 50 wear sunglasses for driving. In a random sample of 20 adults over 50, what is the mean and standard deviation of those that wear sunglasses?

C) mean: 13.8 ; standard deviation: 2.06833266

The ___ probability of an outcome is a probability based on personal judgement.

C) subjective

Given the equation of a regression line is ^y= -3.5x - 2.6, what is the best predicted value for y given x=9.6?

D) -36.20

For a given data set, the equation of the least squares regression line will always pass through

D) X^_ , Y^_

The complement of a 4 heads in the toss of 4 coins is

D) at least one tail

A residual is the difference between

D) the observed value of Y and the predicted value of Y

390 voters are classified by income political party. The results are shown in the table. If a person is selected at random from the sample, find the probability that the person has medium income or votes Democrat.

Short answer: 0.749

According to the government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what was the probability that at least 8 were in a museum?

Short answer: 0.82

Calculate the coefficient of determination to the nearest thousandth, given that the linear correlation coefficient, r, is -0.625. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?

Short answer: The coefficient of determination, R^2 = 0.391. That is, 39.1% of the variation is explained and 60.9% of the variation is unexplained.