Mathematics

Question

Suppose a binomial event has a probability of success of 0.3, and 1250 trials are performed. What is the standard deviation of the possible outcomes? Round your answer to two decimal places.

2 Answer

  • [tex]\sqrt{1250\times0.3\times(1-0.3)}\approx16.20[/tex]
  • Answer: 16.20

    Step-by-step explanation:

    For any binomial event , the formula to calculate the standard deviation of the possible outcomes is given by :-

    [tex]\sigma=\sqrt{\text{p(1-p)n}}[/tex]

    Given: The probability of success p = 0.3

    Then , the probability of failure q= 1-0.3=0.7

    Now,  by using above formula , the standard deviation of the possible outcomes will be :-

    [tex]\sigma=\sqrt{0.3\times0.7\times1250}\\\\\Rightarrow\sigma=\sqrt{262.5}\\\\\Rightarrrow\sigma=16.201851746\approx16.20[/tex]

    Hence, the standard deviation of the possible outcomes = 16.20

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