Question 1

Which of the following probability distributions have the same value for mean, median, and mode​?

Accepted Answer

Normal distribution is symmetric, which means its mean, median, and mode are all located at the center and are equal.

Question 2

There is a lower limit but no upper limit for a random variable that follows the _____ probability distribution.

Accepted Answer

The exponential probability distribution is used to model the time it takes for an event to occur in a Poisson process. It has a lower limit of zero but no upper limit, as it is possible for the event to occur at any point in time. The uniform, normal, and binomial distributions all have both upper and lower limits.

Question 3

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 32 minutes?

Accepted Answer

We need to find the probability of the trip taking more than 32 minutes. We can standardize the random variable X (time taken to travel from home to office) as follows:

Z = (X - μ) / σ

Z = (32 - 25) / 5

Z = 1.4

We can then find the probability using the standard normal distribution table or calculator:

P(Z > 1.4) = 1 - P(Z ≤ 1.4) = 1 - 0.9192 = 0.0808

Therefore, the probability the trip takes more than 32 minutes is approximately 0.0808. The correct choice is D.

Question 4

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes between 20 and 30 minutes?​

Accepted Answer

We need to find the probability that the trip takes between 20 and 30 minutes, which is the same as finding the area under the standard normal curve between z = (20-25)/5 = -1 and z = (30-25)/5 = 1. Using a standard normal table or calculator, we find that the area between z = -1 and z = 1 is approximately 0.6826. Therefore, the probability the trip takes between 20 and 30 minutes is 0.6826.

Question 5

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 40 minutes?​

Accepted Answer

To find the probability that the trip takes more than 40 minutes, we calculate the Z-score for 40 minutes using the formula Z = (X - μ) / σ, where X is 40, μ is 25, and σ is 5. This gives us Z = (40 - 25) / 5 = 15 / 5 = 3. A Z-score of 3 corresponds to a probability of 0.9987 that a value is less than 40 minutes, so the probability of more than 40 minutes is 1 - 0.9987 = 0.0013.

Question 6

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____ random variable.

Accepted Answer

The random variable of speed is measured in miles per hour, which is a continuous measurement. Therefore, the random variable is a continuous random variable.

Question 7

In grading eggs into small, medium, and large, the Nancy Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal.

Accepted Answer

The answer of In grading eggs into small, medium, and...

Question 8

The uniform distribution defined over the interval from 25 to 40 has the probability density function

Accepted Answer

The probability density function (PDF) of a uniform distribution defined over an interval [a, b] is given by f(x) = 1/(b-a) for a ≤ x ≤ b. For the interval from 25 to 40, the length of the interval is 40 - 25 = 15, so the PDF is 1/15 for 25 ≤ x ≤ 40.

Question 9

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked" large" and shrimp that weigh less than 0.47 ounces each into packages marked "small"; the remainder are packed in "medium" size packages. If a day's catch showed that 19.77 percent of the shrimp were large and 6.06 percent were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps' weights are normally distributed.

Accepted Answer

The answer of The Globe Fishery packs shrimp that weigh...

Question 10

The average starting salary of this year's MBA students is $45,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of MBA graduates?

Accepted Answer

The answer of The average starting salary of this year's...

Question 11

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n) _____ probability distribution.

Accepted Answer

The time between successive arrivals follows an exponential probability distribution, which is the appropriate distribution for modeling the interarrival time in a Poisson process.

Question 12

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is _____ distributed.

Accepted Answer

The probability distribution in which the probability is proportional to the length of the interval in which the random variable can assume a value is called a uniform distribution.

Question 13

The probability distribution that can be described by just one parameter is the​

Accepted Answer

The Exponential distribution has just one parameter, which is the mean or rate parameter. The other distributions listed require at least two parameters to fully describe them.

Question 14

The area of the continuous uniform probability distribution is​

Accepted Answer

The continuous uniform probability distribution is a rectangular distribution, as the probability of any outcome within the range of possible values is equal.

Question 15

Which of the following are continuous random variables?​ 
I. The weight of an elephant
II. The time to answer a questionnaire
III. The number of floors in a skyscraper
IV. The square feet of countertop in a kitchen

Accepted Answer

I. Weight of an elephant can take any value between certain range and can be measured accurately to smaller units, hence it is a continuous random variable.
II. Time to answer a questionnaire can also take any value between certain range and can be measured accurately to smaller units, hence it is a continuous random variable.
III. Number of floors in a skyscraper can only take discrete values and cannot be measured accurately to smaller units, hence it is a discrete random variable.
IV. Square feet of countertop in a kitchen can take any value between certain range and can be measured accurately to smaller units, hence it is a continuous random variable.

Question 16

In a normal distribution, it is known that 27.34% of all the items are included from 100 up to the mean, and another 45.99% of all the items are included from the mean up to 145. Determine the mean and the standard deviation of the distribution.

Accepted Answer

The answer of In a normal distribution, it is known...

Question 17

Joe's Record World has two stores and sales at each store follow a normal distribution. For store 1, μ = $2,000 and σ = $200 per day; for store 2, μ = $1,900 and σ = $300 per day. Which store is more likely to have a day's sales in excess of $2200?

Accepted Answer

The answer of Joe's Record World has two stores and...

Question 18

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

Accepted Answer

The answer of A manufacturing process produces items whose weights...

Question 19

In a Poisson probability problem, the rate of errors is one every two hours. To find the probability of three defects in four hours,

Accepted Answer

We use the Poisson probability formula:

P(x; μ) = e^(-μ) * μ^x / x!

where x = number of events and μ = expected number of events.

For four hours, the expected number of errors is:

μ = (rate of errors) * (time) = (1 error/2 hours) * (4 hours) = 2 errors

So, plugging in these values, we get:

P(3; 2) = e^(-2) * 2^3 / 3! = 0.1804

Therefore, the probability of three defects in four hours is 0.1804 or approximately 18.04%.

Out of the given answer choices, only option B has μ = 2 and x = 3.

Question 20

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

Accepted Answer

The answer of A professor at a local university noted...

Quiz 6: Continuous Probability Distributions

Which of the following probability distributions have the same value for mean, median, and mode?

There is a lower limit but no upper limit for a random variable that follows the _____ probability distribution.

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 32 minutes?

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes between 20 and 30 minutes?

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 40 minutes?

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____ random variable.

The uniform distribution defined over the interval from 25 to 40 has the probability density function

The average starting salary of this year's MBA students is $45,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of MBA graduates?

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n) _____ probability distribution.

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is _____ distributed.

The probability distribution that can be described by just one parameter is the

The area of the continuous uniform probability distribution is

Which of the following are continuous random variables? I. The weight of an elephant II. The time to answer a questionnaire III. The number of floors in a skyscraper IV. The square feet of countertop in a kitchen

In a normal distribution, it is known that 27.34% of all the items are included from 100 up to the mean, and another 45.99% of all the items are included from the mean up to 145. Determine the mean and the standard deviation of the distribution.

Joe's Record World has two stores and sales at each store follow a normal distribution. For store 1, μ = $2,000 and σ = $200 per day; for store 2, μ = $1,900 and σ = $300 per day. Which store is more likely to have a day's sales in excess of $2200?

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

In a Poisson probability problem, the rate of errors is one every two hours. To find the probability of three defects in four hours,

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

Quiz 6: Continuous Probability Distributions

Which of the following probability distributions have the same value for mean, median, and mode​?

There is a lower limit but no upper limit for a random variable that follows the _____ probability distribution.

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 32 minutes?

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes between 20 and 30 minutes?​

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 40 minutes?​

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____ random variable.

The uniform distribution defined over the interval from 25 to 40 has the probability density function

The average starting salary of this year's MBA students is $45,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of MBA graduates?

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n) _____ probability distribution.

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is _____ distributed.

The probability distribution that can be described by just one parameter is the​

The area of the continuous uniform probability distribution is​

Which of the following are continuous random variables?​ I. The weight of an elephant II. The time to answer a questionnaire III. The number of floors in a skyscraper IV. The square feet of countertop in a kitchen

In a normal distribution, it is known that 27.34% of all the items are included from 100 up to the mean, and another 45.99% of all the items are included from the mean up to 145. Determine the mean and the standard deviation of the distribution.

Joe's Record World has two stores and sales at each store follow a normal distribution. For store 1, μ = $2,000 and σ = $200 per day; for store 2, μ = $1,900 and σ = $300 per day. Which store is more likely to have a day's sales in excess of $2200?

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

In a Poisson probability problem, the rate of errors is one every two hours. To find the probability of three defects in four hours,

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

Which of the following probability distributions have the same value for mean, median, and mode?

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes between 20 and 30 minutes?

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 40 minutes?

The probability distribution that can be described by just one parameter is the

The area of the continuous uniform probability distribution is

Which of the following are continuous random variables? I. The weight of an elephant II. The time to answer a questionnaire III. The number of floors in a skyscraper IV. The square feet of countertop in a kitchen