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  • The mean and variance of a binomial distribution are 8 and 4 respectively. Find the probability of getting 2 successes in 5 trials.Option: 1 0.41

The mean and variance of a binomial distribution are 8 and 4 respectively. Find the probability of getting 2 successes in 5 trials.

Option: 1

0.41


Option: 2

0.54


Option: 3

0.31


Option: 4

0.25


Answers (1)

best_answer

The mean and variance of a binomial distribution are related by the following formula:
Mean \mathrm{=n^* p-(i)}

i.e. variance \mathrm{=n^* p{ }^* q - (ii)}
From equation (i) and (ii),

\mathrm{q=1 / 2}
Thus, \mathrm{ p=1-q=1 / 2}

The probability of getting 2 successes in 5 trials is given by the following Binomial \mathrm{ ( n, p, k)}  formula:

P(2 successes) \mathrm{ =\operatorname{Binomial}(5,1 / 2,2)}

Using the Binomial coefficient calculator, we can calculate that the probability of getting 2 successes in 5 trials is:


P(2  successes )  \mathrm{ =5 C 2 *(0.5)^{\wedge} 2 *(0.5)^{\wedge} 3=0.256}

Therefore, tffe probability of getting 2 successes in 5 trials is 0.312 .

Posted by

Kuldeep Maurya

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