# Basic Concepts in Probability Distributions

QUESTION 1

A continuous uniform distribution U(100,200) will have the same standard deviation as a continuous uniform distribution U(200,300).

True

False

QUESTION 2

There is a simple formula for normal areas, but we prefer a table for greater accuracy.

True

False

QUESTION 3

The area under a normal curve is 1 only if the distribution is standardized N(0,1).

True

False

QUESTION 4

The area under an exponential curve can exceed 1 because the distribution is right-skewed.

True

False

QUESTION 5

The mean, median, and mode of a normal distribution will always be the same.

True

False

QUESTION 6

A continuous uniform distribution U(0,800) will have Î¼ = 400 and Ïƒ = 230.94.

True

False

QUESTION 7

Any normal distribution has a mean of 0 and a standard deviation of 1.

True

False

QUESTION 8

For a continuous random variable, the total area beneath the PDF will be greater than zero but less than one.

True

False

QUESTION 9

Normal distributions differ only in their means and variances.

True

False

QUESTION 10

The height and width of a continuous uniform distribution's PDF are the same.

True

False

QUESTION 11

The exponential distribution is always skewed right.

True

False

QUESTION 12

If arrivals follow a Poisson distribution, waiting times follow the exponential distribution.

True

False.

https://brainmass.com/statistics/data-collection/basic-concepts-probability-distributions-603157

## SOLUTION This solution is **FREE** courtesy of BrainMass!

QUESTION 1

A continuous uniform distribution U(100,200) will have the same standard deviation as a continuous uniform distribution U(200,300).

Standard deviation in case of U(100,200)=(200-100)/(12)^0.5=28.86751

Standard deviation in case of U(200,300)=(300-200)/(12)^0.5=28.86751

So, Correct option is

True

QUESTION 2

There is a simple formula for normal areas, but we prefer a table for greater accuracy.

False

QUESTION 3

The area under a normal curve is 1 only if the distribution is standardized N(0,1).

False, area under each of the normal curve is 1.

QUESTION 4

The area under an exponential curve can exceed 1 because the distribution is right-skewed.

False, total area should be equal to 1

QUESTION 5

The mean, median, and mode of a normal distribution will always be the same.

True

QUESTION 6

A continuous uniform distribution U(0,800) will have Î¼ = 400 and Ïƒ = 230.94.

Mean=(0+800)/2=400

Standard deviation in case of U(0,800)=(800-0)/(12)^0.5=230.9401

Correct option is True

QUESTION 7

Any normal distribution has a mean of 0 and a standard deviation of 1.

False

QUESTION 8

For a continuous random variable, the total area beneath the PDF will be greater than zero but less than one.

The total area beneath the PDF of a continuous random variable will be equal to 1

False

QUESTION 9

Normal distributions differ only in their means and variances.

True

QUESTION 10

The height and width of a continuous uniform distribution's PDF are the same.

False

QUESTION 11

The exponential distribution is always skewed right.

True

QUESTION 12

If arrivals follow a Poisson distribution, waiting times follow the exponential distribution.

True.

https://brainmass.com/statistics/data-collection/basic-concepts-probability-distributions-603157