Question 1

In a certain very large city, the Department of Transportation (D.O.T.)has organized a complex system of bus transportation.In an advertising campaign, citizens are encouraged to use the new "GO-D.O.T!" system and head for the nearest bus stop to be transported to and from the central city.Suppose that at one of the bus stops the amount of time (in minutes)that a commuter must wait for a bus is a uniformly distributed random variable, T.The values of T run from 0 minutes to 30 minutes. a)Sketch the probability distribution of T. b)What is the probability that a random commuter will spend more than 12 minutes waiting for GO-D.O.T?

Accepted Answer

a)  b)

Question 2

Accepted Answer

True

Question 3

A random variable is discrete if the value of the random variable depends upon the outcome of a chance experiment.

Accepted Answer

A random variable is considered discrete if it can take on a countable number of distinct values, not necessarily because its value depends on the outcome of a chance experiment. Continuous random variables also depend on the outcomes of chance experiments but can take on values in a continuous range.

Question 4

While playing Monopoly, Laura estimated the probabilities of the non-zero rents according to the following probability distribution:  Consider the random variable x = dollar amount in rent in a Monopoly roll. a)If the table above specifies the probability distribution f ()x , what is the mean of the random variable x? b)If the probabilities are associated with the outcomes as in the table above, what is the standard deviation of the random variable x?

Accepted Answer

The answer of While playing Monopoly, Laura estimated the probabilities...

Question 5

One common method used to forecast the results of elections is to take an "exit poll," asking people who they supported as they come out of the voting place.Suppose Smith and Jones are running for City Dogcatcher.In point of fact, 60% of the voting public in the neighborhood of the polling place support Smith.Assuming that the candidate of choice for a voter leaving the polling place is independent of the candidate of choice for the next person to leave, what is the probability that the first 5 voters to leave the polling place would have this sequence for candidate of choice? Smith, Smith, Smith, Jones, Smith

Accepted Answer

The answer of One common method used to forecast the...

Question 6

For a discrete random variable

Accepted Answer

The answer of For a discrete random variable ...

Question 7

In a major study by the statistics classes at Jefferson High School, parking spaces were examined for compliance with the requirement to put money in the meters.Overall, the students found that 80% of metered parking places had meters that had not expired, and 20% had expired.If the traffic officer in charge of ticketing cars with expired meters, and starts at a random location in the City, what is the probability he or she will find an expired meter before the 3rd one?

Accepted Answer

The answer of In a major study by the statistics...

Question 8

For a variable z that has a standard normal distribution, a)W   c)What is the probability that z is between -+1.43 and 1.43 d)What value of z separates the smaller 10% of the standard normal distribution from the larger 90%? e)

Accepted Answer

The answer of For a variable z that has a...

Question 9

For a discrete random variable,

Accepted Answer

The answer of For a discrete random variable, ...

Question 10

A random variable is continuous if the set of possible values includes an entire interval on the number line.

Accepted Answer

A continuous random variable can take on any value within an interval, which means it includes all possible values in that interval.

Question 11

The distribution of all values of a random variable is called a normal distribution.

Accepted Answer

A normal distribution specifically refers to a bell-shaped distribution with a specific mathematical form (mean and standard deviation). There are many other types of distributions that random variables can follow, such as uniform, exponential, or Poisson distributions.

Question 12

Accepted Answer

The answer of ...

Question 13

For a continuous random variable x, the height of the density curve over an interval a to b represents the probability that x is between a and b.

Accepted Answer

The height of the density curve does not represent probability; the area under the curve between a and b represents the probability that x is between a and b.

Question 14

A normal probability plot suggests that a normal probability model is plausible if there is no obvious pattern in the scatter of points.

Accepted Answer

The answer of A normal probability plot suggests that a...

Question 15

For every random variable,

Accepted Answer

The answer of For every random variable, ...

Question 16

In the old Roman Coliseum, two horses would be placed in tandem (side by side)and hitched to a chariot.Since the fast chariots needed to be able to pass the slow chariots, it was of some importance that the horses have room to run, but also they should not be too large.For chariot hitching purposes, the widest measure across a horse occurs in the rump area.The mean rump width is approximately 27" with a standard deviation of about 2".Let random variable w = width in inches across the rump of a randomly selected horse a)The usual length measure as it applies to horses is the "hand," which is by definition equal to 4".Define random variable h = width in hands across the rump of a randomly selected horse.What are the mean and standard deviation of h?

Accepted Answer

The answer of In the old Roman Coliseum, two horses...

Question 17

In a study of the reaction times of left- and right-handers' reaction times to tones delivered to the right ear, the right-handers' scores were approximately normally distributed with a mean of 240 milliseconds and standard deviation of 32 milliseconds.The mean score for right-handers was 210 ms. a)Sketch a normal distribution that describes left-handers' reaction times, and locate the mean reaction time for right-handers in this distribution. b)About what proportion of left-handers reaction times would be "better" (i.e.smaller) than the mean reaction time for right-handers?

Accepted Answer

The answer of In a study of the reaction times...

Question 18

Inspecting meat is a very important part of the process of ensuring healthy food.So that meat inspectors do not fall into a pattern of inspection, they use a 4-sided die to decide whether or not to sample the meat from a particular "side" of beef.The meat inspector rolls the die and if it comes up a 4, a sample is taken of that meat.Forty sides of beef are available for possible inspection.Define random variable x = number of sides selected for inspection out of the 40 available. a)What is the mean of the random variable x? b)What is the standard deviation of the random variable x?

Accepted Answer

The answer of Inspecting meat is a very important part...

Question 19

If random variablesx1and x2 are independent, thenσ22x12+xx=+σσ1 2x2

Accepted Answer

If random variables x1 and x2 are independent, then their covariance is 0. Therefore, the variance of their sum is equal to the sum of their variances.

Question 20

Ifx is a random variable, and random variableyis defined as follows,

Accepted Answer

The answer of Ifx is a random variable, and random...

Quiz 7: Random Variables and Probability Distributions