Now use the binomial formulas below to find the mean and standard deviation when n = 5 and p = 0.02.
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.
- Now use the binomial formulas below to find the
mean and standard deviation when n = 5 and p = 0.02.
![## Understanding Binomial Distribution
### Mean
The mean (denoted by \(\mu\)) of a binomial distribution can be calculated using the formula:
\[ \text{Mean} = \mu = n \cdot p \]
where:
- \(n\) = number of trials
- \(p\) = probability of success on a single trial
### Standard Deviation
The standard deviation (denoted by \(\sigma\)) of a binomial distribution is given by the formula:
\[ \text{Standard Deviation} = \sigma = \sqrt{n p q} \]
where:
- \(n\) = number of trials
- \(p\) = probability of success on a single trial
- \(q\) = probability of failure on a single trial (which is \(1 - p\))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56b89a6c-6ca3-4f25-9a44-1409c69966fc%2Ffa259424-7e6d-461a-a753-1a34e461ec0e%2Fah9nvy5_processed.png&w=3840&q=75)
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