Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
61 Cards in this Set
- Front
- Back
About what percent of the area under the normal curve is within plus two and minus two standard deviation of the mean?
|
95% (95.5%)
|
|
What is a graph of a normal probability distribution called?
|
normal curve
|
|
In a standard normal distribution, ∑ = ______ and σ = ______.
|
zero and one
|
|
What type of probability distribution is the normal distribution?
|
Continuous
|
|
In what units does the standardized z value measure distance from the mean?
|
standard deviation
|
|
What proportion of the area under a normal curve is to the right of a z-score of zero?
|
50% or 0.50
|
|
What does a z value of –2.00 indicate about the corresponding X value?
|
less than or to the left of the mean, or the X value is 2 standard deviations less than the mean
|
|
One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it.
What is this property of the normal curve called? |
asymptotic
|
|
How is the expected value of a uniform distribution computed ?
|
1/(b-a)
|
|
One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it. What is this property of the normal curve called?
|
∑ X/ N
|
|
The shape of any uniform probability distribution is:
A. Negatively skewed B. Positively skewed C. Rectangular D. Bell shaped |
C. Rectangular
|
|
The mean of any uniform probability distribution is:
A. (b - a)/2 B. (a + b)/2 C.∑ X/ῃ D. n^π |
B. (a + b)/2
|
|
The standard deviation of any uniform probability distribution is
A. (b – a)/2 B. n ( 1 – π) C. √[(b-2)^2 / (12)] D. ∑ P(x)(x-ẍ)^2 |
C.√[(b-2)^2 / (12)]
|
|
The upper and lower limits of a uniform probability distribution are
A. positive and negative infinity B. plus and minus three standard deviations. C. 0 and 1 D. the maximum and minimum values of the random variable. |
D. the maximum and minimum values of the random variable.
|
|
What is an important similarity between the uniform and normal probability distributions?
A. The mean, median and mode are all equal. B. The mean and median are equal C. They are negatively skewed D. About 68% of all observations are within one standard deviation of the mean. |
The mean and median are equal
|
|
Which of the following is NOT true regarding the normal distribution?
A. Mean, median and mode are all equal B. It has a single peak C. It is symmetrical D. The points of the curve meet the X-axis at z = –3 and z = 3 |
D. The points of the curve meet the X-axis at z = –3 and z = 3
|
|
For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what
percent of the observations? A. 50% B. 99.7% C. 95% D. 68% |
C. 95%
|
|
Which of the following is NOT a characteristic of the normal probability distribution?
A. Positively-skewed B. Bell-shaped C. Symmetrical D. Asymptotic |
A. Positively-skewed
|
|
What is the proportion of the total area under the normal curve within plus and minus two standard
deviations of the mean? A. 68% B. 99.7% C. 34% D. 95% |
D. 95%
|
|
Which of the following is true in a normal distribution?
A. Mean equals the mode and the median B. Mode equals the median C. Mean divides the distribution into two equal parts D. All of the above are correct |
D. All of the above are correct
|
|
Tables of normal distribution probabilities are found in many statistics books. These probabilities are
calculated from a normal distribution with A. a mean of 1 and a standard deviation of 1 B. a mean of 100 and a standard deviation of 15 C. a mean of 0 and a standard deviation of 15 D. a mean of 0 and a standard deviation of 1 |
D. a mean of 0 and a standard deviation of 1
|
|
Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second
normal distribution has a mean of 10 and a standard deviation of 2. Which of the following it true? A. the locations of the distributions are different B. the distributions are from two different families C. the dispersions of the distributions are different D. the dispersions of the distributions are the same |
A. the locations of the distributions are different
|
|
A random variable from an experiment where outcomes are normally distributed
A. can have any value between -∞ and +∞ B. can have only a few discrete values C. can have a mean of 0 and a standard deviation of 1 D. can have no values |
A. can have any value between -∞ and +∞
|
|
The total area of a normal probability distribution is
A. between –3.0 and 3.0 B. 1.00 C. dependent on a value of 'z'. D. approximated by the binomial distribution. |
B. 1.00
|
|
An area of a normal probability distribution represents
A. a permutation B. a combination C. a likelihood D. a shaded area |
C. a likelihood
|
|
The standard normal probability distribution is one which has:
A. A mean of 1 and any standard deviation B. Any mean and a standard deviation of 1 C. A mean of 0 and any standard deviation D. A mean of 0 and a standard deviation of 1 |
D. A mean of 0 and a standard deviation of 1
|
|
What is the distribution with a mean of 0 and a standard deviation of 1 called?
A. Frequency distribution B. z-score C. Standard normal distribution D. Binomial probability distribution |
C. Standard normal distribution
|
|
True or False:
The Empirical Rule of probability can be applied to the uniform probability distribution. |
False
|
|
True or False:
Areas within a continuous probability distribution represent probabilities. |
True
|
|
True or False:
The total area within a continuous probability distribution is equal to 100. |
False
|
|
True or False:
The total area within any continuous probability distribution is equal to 1.00 |
True
|
|
True or False:
For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed. |
False
|
|
True or False:
The uniform probability distribution's standard deviation is proportional to the distribution's range. |
True
|
|
True or False:
For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed. |
True
|
|
True or False:
For a uniform probability distribution, the probability of any event is equal to 1/(b-a). |
False
|
|
True or False:
For any uniform probability distribution, the mean and standard deviation can be computed by knowing the maximum and minimum values of the random variable. |
True
|
|
True or False:
In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. |
True
|
|
True or False:
The uniform probability distribution is symmetric about the mode. |
False
|
|
True or False:
Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it. |
True
|
|
True or False:
The uniform probability distribution's shape is a rectangle. |
True
|
|
True or False:
The uniform probability distribution is symmetric about the mean and median. |
True
|
|
True or False:
A continuity correction factor compensates for estimating a discrete distribution with a continuous distribution. |
True
|
|
True or False:
When referring to the normal probability distribution, there is not just one; there is a "family" of distributions. |
True
|
|
True or False:
Some normal probability distributions have equal arithmetic means, but their standard deviations may be different. |
True
|
|
True or False:
The normal curve falls off smoothly in either direction from the central value. Since it is asymptotic, the curve gets closer and closer to the X-axis, but never actually touches it. |
True
|
|
True or False:
The area under the normal curve within plus and minus one standard deviation of the mean is about 68.26%. |
True
|
|
True or False:
Some normal probability distributions have different arithmetic means and different standard deviations. |
True
|
|
True or False:
For a normal probability distribution, about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area under the normal curve is within three standard deviations of the mean. |
True
|
|
True or False:
Some normal probability distributions are positively skewed. |
False
|
|
True or False:
A z-score is the distance between a selected value (X) and the population mean (µ ) divided by the population standard deviation (σ ). |
True
|
|
True or False:
In terms of a formula the standardized value of z is found by z = (X –µ )/σ . |
True
|
|
True or False:
The total area under the normal curve is 100%. |
True
|
|
True or False:
The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when ῃ π ῃ(1-π) are both greater than five. |
True
|
|
True or False:
The number of different normal distributions is unlimited. |
True
|
|
True or False:
The mean (µ ) divides the normal curve into two identical halves. |
True
|
|
True or False:
The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1. |
True
|
|
True or False:
A z-score is also referred to as the standard normal deviate or just the normal deviate. |
True
|
|
True or False:
The mean of a normal distribution is represented by σ. |
False
|
|
True or False:
A computed z for X values to the right of the mean is negative. |
False
|
|
True or False:
A computed z for X values to the left of the mean is positive. |
False
|
|
True or False:
The number of different standard normal distributions is unlimited. |
False
|