Calculate the standard deviation, round the standard deviation to 3 decimal X 0 1 2 3 4 5 Total P(x) .04 .33 .27 .21 .13 .02 1.00
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Calculate the standard deviation, round the standard deviation to 3 decimal
X 0 1 2 3 4 5 Total
P(x) .04 .33 .27 .21 .13 .02 1.00
- The formula of the variance σ2 of a discrete random variable X is
σ2=∑(x−μ)2P(x) .
Here x represents values of the random variable X, μ is the mean of X, P(x) represents the corresponding probability, and symbol ∑ represents the sum of all products (x−μ)2P(x).
- To find the standard deviation, σ, of a discrete random variable X, simply take the square root of the variance σ2.
σ==
Given : The following table shows the provided outputs of the discrete random variables, along with the corresponding probabilities :
| 0 | 0.04 |
| 1 | 0.33 |
| 2 | 0.27 |
| 3 | 0.21 |
| 4 | 0.13 |
| 5 | 0.02 |
Now, we need to multiply the corresponding outcomes with the corresponding probabilities, in order to compute the population mean :
| 0 | 0.04 | |
| 1 | 0.33 | |
| 2 | 0.27 | |
| 3 | 0.21 | |
| 4 | 0.13 | |
| 5 | 0.02 |
Therefore, the population mean is calculated as follows :
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