What are the mean and standard deviation of a binomial

zakinutuzi

zakinutuzi

Answered question

2022-01-16

What are the mean and standard deviation of a binomial probability distribution with n=17 and p=1832?

Answer & Explanation

Kirsten Davis

Kirsten Davis

Beginner2022-01-16Added 27 answers

Explanation:
Unless you have to calculate everything each time, we could simply use known formulas.
In binomial distribution the mean is given by np and variance by np(1-p).
Since in our case n=17 and p=1832=916 the mean is
17916=15316=9.5 and variance is 17916(1916)=1071256. Standard deviation is the square root of variance so we have 1071256=3119162.0454.
ramirezhereva

ramirezhereva

Beginner2022-01-17Added 28 answers

Solution:
The mean of the binomial distribution is interpreted as the mean number of successes for the distribution. To find the mean, use the formula
μ=np
where n is the number of trials and p is the probability of success on a single trial. Substituting values for this problem, we have
μ=171832
Multiplying the expression we have
μ=9.52
The standard deviation of the binomial distribution is interpreted as the standard deviation of the number of successes for the distribution. To find the standard deviation, use the formula
σ=np(1p)
where n is the number of trials and p is the probability of success on a single trial. Substituting values fo this problem, we have
σ=171832(11832)
Evaluating the expression on the right, we have
σ=4.1888
σ=2.0454

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