Ch. 7
True or false: A continuous random variable can have a finite set of integer values.
False - continuous RV's are defined on intervals
The PDF of the continuous uniform distribution has which shape?
Rectangular
For a continuous distribution, the standard deviation is the __________ ___________of the variance
Square root
An example of a random variable that closely follows the normal distribution is ______________.
Weight of a box of cookies because it's symmetric about the average, unimodal; weights of newborn babies
A random variable is said to be continuous if it
Can have decimal values and is measured over an interval.
Any normal random variable X can be standardized by subtracting the __________ from x then dividing by the ________________ ___________
Mean; standard deviation
The z score associated with the lowest 2.5% of a normal distribution will be
Negative - cumulative areas less than 50% have negative z scores.
Because the standard normal distribution is symmetrical about the mean 0, P(0 ≤ Z ≤ 1.96) is the same as
P(-1.96 ≤ Z ≤ 0)
It is meaningful to compute the probability that a continuous random variable
Is greater/less than or equal to a number or between two numbers
Which of the following is an example of a continuous random variable?
Binomial
True or false: The uniform model is used only when you have no reason to imagine that any X-values are more likely than others.
True
One characteristic of a well-defined probability density function of a continuous random variable X is that the area under the curve, f(x,) over all values of x is
equal to one.
To find the z score associated with the highest 1% of a normal distribution, recognize that the area to the left of this z score is
.99
The z score associated with the highest 10% is closest to
1.28
A random variable with the continuous uniform distribution has which of the following characteristics?
An equally likely chance of assuming any value within a specified range.
For normally distributed random variables, how would one verify the empirical rule percentages using z scores?
Find P(-1 ≤ Z ≤ 1) from a standard normal table and compare to 68%.
The normal distribution is the most extensively used distribution in statistical studies because
Many physical measurements have a bell-shaped distribution, economic and financial data often display bell-shaped distributions and it has important features used in sampling and estimation
What is the use of the cumulative distribution function, F(x), of a continuous random variable?
To find the probability that X is less than or equal to any value x.
Binomial probabilities can be difficult to calculate, and therefore appropriate to approximate, when
n is large.
The normal distribution is asymptotic in the sense that _____________
the tails get closer and closer to the horizontal axis, but never touch it.
The probability that a continuous random variable equals any of its values is
zero
To find P(0 ≤ Z ≤ 1.37) using Appendix C-1, find the row containing ______ in the far left column. Then find the column containing _________ in the top row.
1.3; .07
The probability that a continuous random variable takes on a particular value is zero because of which of the following reasons?
The area under a curve AT a certain point is zero.
A random variable is said to be discrete if it has _____
countable number of values.
The function used to find the area under the f(x) of a continuous random variable X up to any value x is called
the cumulative distribution function or CDF.
Which of the following statements from the empirical rule is correct?
Approximately 95% of values fall within 2 standard deviations of the mean for data with bell shaped histogram.
Which of the following is an example of a discrete random variable? Exponential, normal, continuous uniform, binomial
Binomial
A random variable with an equally likely chance of assuming any value within a specified range is said to have which distribution?
Continuous uniform distribution.
The Normal distribution is also called the ______ distribution.
Gaussian
It is appropriate to approximate the Poisson distribution with the normal distribution when
λ is large.
To approximate the binomial distribution with the normal distribution let
μ = nπ and σ = nπ(1−π)
To approximate the Poisson distribution with the normal distribution let
μ = λ and σ = sqrt(λ)
One condition of a well-defined probability density function of a continuous random variable X is that f(x) is
greater than zero for all values of X.
Which of the following statements about the variance of a continuous random variable are true?
The variance is the weighted average of the squared deviations from the mean and the standard deviation is the square root of the variance
True or false: Under appropriate circumstances, many discrete random variables can be described by the normal distribution.
True
Would X = [0,500] satisfy the definition of a continuous random variable?
Yes
Consider a random variable X that denotes a random delivery time anywhere between 9 am and 10 am. X would reasonably be
a continuous uniform random variable.
The probability that a discrete random variable equals any of its values is
between zero and one, inclusive.
The normal distribution tails ____________
never touch the horizontal axis.
The standard deviation of the standard normal distribution is ______?
one
