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What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively
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What is the number of trials of a binomial distribution having mean an...
Calculating the Number of Trials in a Binomial Distribution


Assuming the mean and standard deviation of a binomial distribution as 3 and 1.5 respectively, we can calculate the number of trials in the following manner:


Step 1: Identify the formula for mean and standard deviation of a binomial distribution


The mean and standard deviation of a binomial distribution can be calculated using the following formulas:



  • Mean = n * p

  • Standard deviation = sqrt(n * p * q)



where n is the number of trials, p is the probability of success, and q is the probability of failure.


Step 2: Substitute the given values of mean and standard deviation


Substituting the given values of mean and standard deviation in the above formulas, we get:



  • 3 = n * p

  • 1.5 = sqrt(n * p * q)



Step 3: Solve for p and q


From the first equation, we can solve for p as:



  • p = 3 / n



Substituting this value of p in the second equation, we get:



  • 1.5 = sqrt(n * (3 / n) * q)

  • 1.5 = sqrt(3q)

  • 2.25 = 3q

  • q = 0.75



Step 4: Substitute the values of p and q in the first equation


Substituting the values of p and q in the first equation, we get:



  • 3 = n * (3 / n)

  • n = 3 / (3 / n)

  • n = 9



Step 5: Interpretation


Therefore, the number of trials in the binomial distribution is 9. This means that the experiment was repeated 9 times to obtain the given mean and standard deviation.
Community Answer
What is the number of trials of a binomial distribution having mean an...
Ans: n=12;. np=3, root of npq=1.5, q=0.75, p=0.25, p=1-q. then n=12
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What is the number of trials of a binomial distribution having mean and standard deviation as 3 and 1.5 respectively
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