The distance between the middle and the inflection point is the standard deviation.
The mean must be 0 and the standard deviation must be 1. Use the formula: z = (x - mu)/sigma
Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).
It is impossible to answer the question because "the following" did not follow.
The area under the standard normal curve is 1.
In a normal distribution, approximately 95% of the population falls within 2 standard deviations of the mean. This is known as the 95% rule or the empirical rule. The empirical rule states that within one standard deviation of the mean, about 68% of the population falls, and within two standard deviations, about 95% of the population falls.
Mean = 0 Standard Deviation = 1
1
nop its not
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.
It is 15 points.
No, they are rarely the same.
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
Yes, that's true. In a normal distribution, a smaller standard deviation indicates that the data points are closer to the mean, resulting in a taller and narrower curve. Conversely, a larger standard deviation leads to a wider and shorter curve, reflecting more variability in the data. Thus, the standard deviation directly affects the shape of the normal distribution graph.
Because the standard deviation is one of the two parameters (the other being the mean) which define the Normal curve. The mean defines the location and the standard deviation defines its shape.
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.
The width of the peak of a normal curve depends primarily on the standard deviation of the distribution. A larger standard deviation results in a wider and flatter curve, indicating greater variability in the data, while a smaller standard deviation yields a narrower and taller peak, indicating less variability. Thus, the standard deviation is crucial for determining the spread of the data around the mean.
When the normal curve is plotted using standard deviation units, each with a value of 1.00, it is referred to as the standard normal distribution. In this distribution, the mean is 0 and the standard deviation is 1, allowing for easy comparison of different data sets by transforming them into z-scores. The standard normal distribution is often represented by the symbol Z.