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Which normal distribution is also the standard normal curve?
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
Describe the properties of a normal distribution?
A normal distribution is symmetric and when looked at on a graph, the graph looks like a bell shaped curve. Approximately 95 percent of its values should lie within two standard deviations of the mean. Frequency of the data lies mostly in the middle of the curve.
What is the area under the standard normal distribution curve between z1.50 and z2.50?
~0.0606
How the normal distribution could be transformed to a standard normal distribution?
You may transform a normal distribution curve, with, f(x), distributed normally, with mean mu, and standard deviation s, into a standard normal distribution f(z), with mu=0 and s=1, using this transform: z = (x- mu)/s
Why if a probability distribution curve is bell shaped why is this a normal distribution?
A bell shaped probability distribution curve is NOT necessarily a normal distribution.
Normal curve is the meaning of standard normal distribution?
No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
How does the bell curve relates to the empirical rule?
The bell curve, also known as the normal distribution, is a symmetrical probability distribution that follows the empirical rule. The empirical rule states that for approximately 68% of the data, it lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations when data follows a normal distribution. This relationship allows us to make predictions about data distribution based on these rules.
Which normal distribution is also the standard normal curve?
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
What is true in about a normal distribution?
A normal distribution is a symmetric, bell-shaped curve characterized by its mean and standard deviation. Approximately 68% of the data falls within one standard deviation from the mean, about 95% within two standard deviations, and around 99.7% within three standard deviations, commonly referred to as the empirical rule. Additionally, the mean, median, and mode of a normal distribution are all equal and located at the center of the distribution. This property makes the normal distribution fundamental in statistics and probability theory.
What is the mean and standard deviations and the standard normal distribution?
Mean is the average, sum total divided by total number of data entries. Standard deviation is the square root of the sum total of the data values divided by the total number of data values. The standard normal distribution is a distribution that closely resembles a bell curve.
Describe the properties of a normal distribution?
A normal distribution is symmetric and when looked at on a graph, the graph looks like a bell shaped curve. Approximately 95 percent of its values should lie within two standard deviations of the mean. Frequency of the data lies mostly in the middle of the curve.
What is the mean of standard normal curve?
The mean of a standard normal curve is 0. This curve, which is a type of probability distribution known as the standard normal distribution, is symmetric and bell-shaped, centered around the mean. Additionally, the standard deviation of a standard normal curve is 1, which helps define the spread of the data around the mean.
What percentage of scores falls between the mean and -2 to 2 standard deviations under the normal curve?
In a normal distribution, approximately 68% of scores fall within one standard deviation of the mean (between -1 and +1 standard deviations). About 95% of scores fall within two standard deviations (between -2 and +2 standard deviations). Therefore, the percentage of scores that falls specifically between the mean and -2 to 2 standard deviations is about 95% minus the 50% that is below the mean, resulting in approximately 45%.
What are three characteristics of a normal curve?
A normal curve, or Gaussian distribution, is symmetric and bell-shaped, indicating that the data is evenly distributed around the mean. It has a mean, median, and mode that are all equal and located at the center of the curve. Additionally, approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and around 99.7% within three standard deviations, known as the empirical rule.
What does normality mean in health and social care?
All minor deviations occurring with two standard deviations under the Gaussian curve are considered normal. Deviations occurring outside of two standard deviations are considered abnormal.
What is the difference between a general normal curve and a standard normal curve?
A standard normal distribution has a mean of zero and a standard deviation of 1. A normal distribution can have any real number as a mean and the standard deviation must be greater than zero.
What is the proportion of the total area under the normal curve within plus or minus 2 standard deviations?
95%
