I need help figuring out this mean and standard deviation? Find the mean and standard deviation for a bionomial experiment where n=260, p=0.675 a. u=260 a=7.55 b. u=260 a=57.04 c. u=175.50...

I need help figuring out this mean and standard deviation? Find the mean and standard deviation for a bionomial experiment where n=260, p=0.675 a. u=260 a=7.55 b. u=260 a=57.04 c. u=175.50 a=7.55 d. u=97.50 a=13.25 e. u=175.50 a=9.19

Asked on by mlunar74

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

We are given `n=260` and `p=.675` for a binomial experiment.

(1) Since `p=.675` we know that `q=1-.675=.325` (p is the proportion that has the quality we seek, q is the proportion without the quality. They are complements thus the probabilities sum to 1)

(2) The mean `mu` is given by `mu=n*p` , so `mu=260*.675=175.5`

You really don't need the formula for this. Here the mean is also the expected value -- if I told you that 67.5% of fish were red, and that there were 260 fish you would tell me that 175.5 of the fish were red.

(3) The standard deviation `sigma` is given by `sigma=sqrt(n*p*q)` so `sigma=sqrt(260*.675*.325)=sqrt(57.035)~~7.55`

Alright, you need the formula for that.

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Given `n=260,p=.675` then `mu=175.5,sigma~~7.55` so the answer is (c)

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(a) has n and the correct s.d.

(b) has n and the variance

(c) correct

(d) you are in trouble

(e) correct mean, not sure at all how you get that s.d.

Sources:

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