# What are the mean and standard deviation of a binomial probability distribution with #n=11 # and #p=7/30 #?

Mean is

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The mean (( \mu )) of a binomial distribution is calculated using the formula ( \mu = np ), where ( n ) is the number of trials and ( p ) is the probability of success in each trial.

Given ( n = 11 ) and ( p = \frac{7}{30} ), we have: [ \mu = 11 \times \frac{7}{30} = \frac{77}{30} ]

The standard deviation (( \sigma )) of a binomial distribution is calculated using the formula ( \sigma = \sqrt{np(1-p)} ).

Substituting the given values: [ \sigma = \sqrt{11 \times \frac{7}{30} \times \left(1 - \frac{7}{30}\right)} ] [ \sigma = \sqrt{11 \times \frac{7}{30} \times \frac{23}{30}} ] [ \sigma = \sqrt{\frac{161}{150}} ]

Therefore, the mean (( \mu )) is ( \frac{77}{30} ) and the standard deviation (( \sigma )) is ( \sqrt{\frac{161}{150}} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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