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# Basic Concepts in Probability Distributions

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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 μ = 400 and σ = 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.

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## 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 μ = 400 and σ = 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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com September 26, 2022, 9:07 am ad1c9bdddf>
https://brainmass.com/statistics/data-collection/basic-concepts-probability-distributions-603157