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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.
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True or False are the mean median and mode all equal for a normal distribution?
True. You can find many references including wikipedia on the Normal distribution on the internet.
If the mean of a normal distribution i s105 what is the median of the distribution?
In a normal distribution, the mean, median, and mode are all equal. Therefore, if the mean of the distribution is 105, the median of the distribution is also 105. This property holds true for any normal distribution regardless of its standard deviation.
In the standard normal distribution the variance is always 1?
true
Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
If the mean is 40 in a normal distribution what is the median?
In a normal distribution, the mean, median, and mode are all equal. Therefore, if the mean is 40, the median is also 40. This property holds true for any normal distribution regardless of its specific values.
What is true regarding the normal distribution?
It is symmetrical
True or False are the mean median and mode all equal for a normal distribution?
True. You can find many references including wikipedia on the Normal distribution on the internet.
Normal distribution it is always true that mean equals median equals mode?
Yes- this can be proved from the normal distribution function.
Is it true that the curve for the normal distribution is symmetrical in respect to the mean?
yes it is true
If the mean of a normal distribution i s105 what is the median of the distribution?
In a normal distribution, the mean, median, and mode are all equal. Therefore, if the mean of the distribution is 105, the median of the distribution is also 105. This property holds true for any normal distribution regardless of its standard deviation.
In the standard normal distribution the variance is always 1?
true
Are these true of normal probability distribution IIt is symmetric about the mean TTotal area under the normal distribution curve is equal to 1 DDistribution is totally described by two quantities?
Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.
Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
If a probability distribution curve is bell-shaped then this is a normal distribution?
True * * * * * No. The Student's t-distribution, for example, is also bell shaped.
Is it true some normal probability distributions are positively skewed?
No. The Normal distribution is symmetric: skewness = 0.
If the mean is 40 in a normal distribution what is the median?
In a normal distribution, the mean, median, and mode are all equal. Therefore, if the mean is 40, the median is also 40. This property holds true for any normal distribution regardless of its specific values.
True or False If the population distribution is unknown in most cases the sampling distribution of the mean can be approximated by the normal dist. if the samples contain at least 30 observations.?
true
