What are the mean and standard deviation of a binomial

kuvitia9f

kuvitia9f

Answered question

2022-01-16

What are the mean and standard deviation of a binomial probability distribution with n=169 and p=113?

Answer & Explanation

Fasaniu

Fasaniu

Beginner2022-01-16Added 46 answers

Explanation:
Mean and standard deviation of a binomial probability distribution are given by np and npq where q=1-p.
In the given distribution, n=169 and p=113. hence q=1p=1113=1213.
Hence, mean is 169113 i.e. 13 and standard deviation is 169(113)(1213)
or 12=3.464.
lenkiklisg7

lenkiklisg7

Beginner2022-01-17Added 29 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=169113
Multiplying the expression we have
μ=12.8
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 umber of trials and p is the probability of success on a single trial. Substituting values fo this problem, we have
σ=169113(1113)
Evaluating the expression on the right, we have
σ=11.8
σ=3.46

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