MAT-133 Statistics Chapter 7.1-7.4
Choose the correct Excel function to find P(X > 110) for a normal random variable with μ = 100 and σ = 20.
1-NORM.DIST(110,100,20,1)
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 from the empirical rule is correct?
Approximately 95% of values fall within 2 standard deviations of the mean for data with bell shaped histogram.
NORM.S.DIST NORM.DIST
Area to the left of a z score Area to the left of a given x value
Which of the following is an example of a discrete random variable?
Binomial.
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 ___
Blank 1 = 1.3 Blank 2= 0.07
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).
Blank 1: -1.6 Blank 2: .05 Blank 3: .0495
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.
True or false: 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.
Which Excel expression would be used to find the X value associated with the highest 10% if X has a mean = 100 and a standard deviation = 20?
NORM.INV(.90,100,20)
Choose the correct Excel function to find P(Z ≤0.87)
NORM.S.DIST(.87,1)
Which Excel expression would be used to find the Z score associated with the lowest 2.5%?
NORM.S.INV(.025)
Which of the following is an example of a continuous random variable?
Normal
The standard deviation of the standard normal distribution is ______?
One
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)
Which probability statement below represents a cumulative probability?
P(Z ≤ -2.34)
An example of a random variable that closely follows the normal distribution is ______________.
The weight of a box of cookies
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.
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
True or false: 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]
27. The letter used to denote the standard normal random variable is
Z
The probability that a continuous random variable equals any of its values is
Zero
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.
The normal distribution is the most extensively used distribution in statistical studies because
economic and financial data often display bell-shaped distributions. it has important features used in sampling and estimation. many physical measurements have a bell-shaped distribution.
The normal distribution tails ____
never touch the horizontal axis.
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.
The normal distribution is asymptotic in the sense that _____________
the tails get closer and closer to the horizontal axis, but never touch it.
The purpose of standardizing a normal random variable is
to create a common scale that then can be used for finding probabilities using tables or Excel.
An example of a random variable that closely follows the normal distribution is
weights of newborn babies.
