What are the mean and standard deviation of a binomial probability distribution with #n=5 # and #p=4/7 #?

Answer 1

Mean is #2.857# and standard deviation is #1.107#

Mean of a binomial probability distribution is given by #np# and standard deviation is given by #sqrtnpq#, where #q=1-p#.
In the given example, #np=5*4/7=20/7=2.857#,
As #q=1-4/7=3/7#, #sqrtnpq=sqrt(5*4/7*3/7)=1/7*sqrt60=2sqrt15/7=1.107#
Hence mean is #2.857# and standard deviation is #1.107#
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Answer 2

The mean ((\mu)) of a binomial probability distribution is calculated using the formula:

[ \mu = n \times p ]

where (n) is the number of trials and (p) is the probability of success on each trial.

The standard deviation ((\sigma)) of a binomial probability distribution is calculated using the formula:

[ \sigma = \sqrt{n \times p \times (1 - p)} ]

Substituting (n = 5) and (p = \frac{4}{7}) into the formulas, we can find the mean and standard deviation:

Mean ((\mu)): [ \mu = 5 \times \frac{4}{7} ]

Standard deviation ((\sigma)): [ \sigma = \sqrt{5 \times \frac{4}{7} \times \left(1 - \frac{4}{7}\right)} ]

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Answer from HIX Tutor

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.

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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