Continuous Probability Distributions
To find the P(Z ≤ -1.65) find the row containing _____ in the far left column. Then find the column containing _____ in the top row. The intersection of this row and column is _____ (Round to 4 decimals).
-1.6 .05 .0495
For a continuous random variable X with a = 10 and b = 20, P(X ≤ 14) =
.4
To find the P(Z > 0.93) find the row containing _____ in the far left column. Then find the column containing _____ in the top row. P(Z > 0.93) = 1 - _____ (round to 4 decimals) = (round to 4 decimals).
.9 .03 .8238 .1762
When using a standard normal table, P(-2 ≤ Z ≤ 2) is
.9544
The probability that a continuous random variable equals any of its values is:
0
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.
A continuous random variable can have a finite set of integer values.
False
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 also called the ______ distribution.
Gaussian
Which of the following characteristics does NOT describe a Normal distribution?
It has finite upper and lower limits.
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)
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.
The standard deviation of the standard normal distribution is ______.
one
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
An example of a random variable that closely follows the normal distribution is
weight of newborn babies
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
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.
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. The standard deviation is the square root of the variance.
The sums of probabilities over groups of points are taken for discrete random variables.
True
The uniform model is used only when you have no reason to imagine that any X-values are more likely than others.
True
Under appropriate circumstances, many discrete random variables can be described by the normal distribution.
True
Which of the following sample spaces would satisfy the definition of a continuous random variable?
X = [0,500]
The letter used to denote the standard normal random variable is
Z
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.
A random variable is said to be continuous if it
can have decimal values. is measured over an interval.
A random variable is said to be discrete if it has _____
countable number of values.
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
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.
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. it has important features used in sampling and estimation.
