Chapter 7
Select all that apply Which statements below accurately characterize a uniform distribution. Select all that apply
- areas within the distribution represent probabilities - the area inside the rectangle (i.e the frequency polygon) must be one
Select all that apply Which statements describe the mean of a Uniform Distribution. Select all that apply
- it is always in the middle of the minimum and maximum values - it is always equal to the median
Choose the three characteristics from the following list that describe the exponential distribution.
- it is characterized by only one parameter, known as the "rate" parameter - the random variable is always positive - the distribution is asymmetrical and positively skewed
Which of the following statements are true with respect to both the Standard Normal distribution and any normal probability distribution? Choose all that apply
- the areas are equal to 1 - a normal probability distribution can be converted into a standard normal distribution
Suppose you have two normal distributions: one has μ = 16 and σ = 2 and the other has μ = 20 and σ = 3. Which of the following statements are true? Select all that apply
- the distribution with the mean of 20 is to the right of the other distribution - the distribution with the standard deviation of 2 is more peaked
Which of the following are true because the normal probability distribution is symmetric about the mean? Select all that apply
- the shape to the left of the mean is a mirror image of the shape to the right of the mean - the area on each side of the mean equals one half
Which of the following statements are true of the Standard Normal Distribution?
- the standard deviation is 1 - the mean is zero
What is the purpose of converting a random variable to a z-value? Select all that apply
- to compare a normal distribution to a standard normal distribution - to express the distance from the mean in terms of the standard deviation
How would you describe the shape of the Normal Distribution?
It is "bell" shaped, and symmetrical with the center at μ
A Uniform Distribution has the same probability for any x such that a≤x≤b. What is this probability?
P(x) = 1/b−a
Which of the following formulas describes the Exponential distribution?
P(x) = λe-λx
The average score on an IQ test is 110 and the standard deviation is 10 grams. What is the z-value for a score of 130?
z = 2
The formula for converting a normally distributed random variable X, to a z-value is z = X−μσX-μσ. Match the variables to their description
z- a standard normal random variable a standard normal random variable X- a normal random variable a normal random variable μ- the mean of X the mean of X σ- the standard deviation of X the standard deviation of X
A Uniform distribution has a minimum value for the random variable of "a" and a maximum of "b". What is the formula for the mean?
μ = a+b/2
What are the upper and lower limits of the random variable for the Normal distribution?
no limits, it is asymptotic in both directions
Which of the following is the best description of the shape of a uniform distribution?
rectangular
Since the normal probability distribution is symmetrical about the mean, which of the following is true?
the area on each side of the mean is 0.5
Which is the best definition of the z-value?
the distance between a value x and the mean divided by the standard deviation
What determines the width and location of the Normal Distribution?
the mean (μ) determines the location and the standard deviation (σ) determines the width
Which one of the following is a result of the normal probability distribution being bell-shaped?
the mean, median, and mode are at the center
Which one of the following items of information is required to fully define a uniform distribution?
the minimum and maximum value of the variable
For a uniform distribution, the probability is defined as P(x) = 1b−a1b-a. What do the symbols b and a represent?
the minimum and maximum values
Which one of the following is true about the uniform distribution?
the minimum is identified as 'a' and the maximum is identified as 'b'.
Which of the following random experiments could not be described by an exponential distribution?
the probability that 5 customers will use the bank's ATM in the next hour
Which of the following is an example of a continuous random variable?
the square footage of a house
The area under a uniform distribution (or any probability distribution) represents a probability. Which one of the following statements characterizes this area?
the total area is one
What kind of events are described by an Exponential distribution?
times between events in a sequence
The duration of a red light at a particular intersection in a city is uniformly distribution from one to four minutes. What is the probability that you will wait at the particular red light between 2.5 and 3 minutes?
1/6
The duration of a red light at a particular intersection in a city is uniformly distribution from one to four minutes. Match the numbers to the parameters for this distribution
3- range 2.5- mean 0.87- standard deviation 0.33- p(x)
Which of the following is true regarding continuous and discrete random variables?
continuous random variables usually result from measuring
Where does the curve of the normal distribution touch the x-axis?
it never touches, but approaches asymptotically in both directions
