Normal distribution, also known as the Gaussian distribution, is aprobability distributionthat is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. The normal distribution appears as a "bell curve" when graphed. Key Takeaways ...
Normal distributions are used when the population distribution is assumed to be normal. The t-distribution is similar to the normal distribution, just with fatter tails. Both assume a normally distributed population. T-distributions thus have higher kurtosis than normal distributions. The probability of...
A normality test determines whether a sample data has been drawn from a normally distributed population. It is generally performed to verify whether the data involved in the research have a normal distribution. Many statistical procedures such as correlation, regression, t-tests, and ANOVA, namely ...
Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54. Given that X is normally distributed with a mean of 0.545 and a stan...
A continuous probability distribution that is perfectly symmetrical about a mean and widely used for purposes in statistics. It is used to describe the behavior of random variables which have been normally distributed. The PDF of a normal distribution, the so-called Gaussian distribution, is expresse...
Suppose that X is normally distributed with a mean of 50 and a standard deviation of 8. What is P(X≤65.60)? Normal Distributions: A normally distributed random variable X with mean μ and standard deviation σ can be converted to a...
The ideal of a normal distribution is also useful as a point of comparison when data are not normally distributed. For example, most people assume that the distribution of household income in the U.S. would be a normal distribution and resemble the bell curve when plotted on a graph. This...
Given a standardized test that is normally distributed with mean of 80 and standard deviation of 12, find P(X less than 62). A normal distribution has a mean of 44 and a standard deviation of 4. What is the probability that a value drawn...
1.11 A bank’s profit next year will be normally distributed with a mean of 0.6% of assets and a standard deviation of 1.5% of assets. The bank’s equity is 4% of assets. What is the probability that the bank will have a positive equity at the end of the year? Ignore taxes.1....
Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8. What is the probability that a randomly chosen score is between 70 and 80? Scores on a statistics ...