Questions: For this binomial distribution, what is the Expected Value for the number of successes when sample size is 82 with a probability of 0.39 ?
Add your answer
integer, decimat, or Enotation allowed
Transcript text: For this binomial distribution, what is the Expected Value for the number of successes when sample size is 82 with a probability of 0.39 ?
Add your answer
integer, decimat, or Enotation allowed
Solution
Solution Steps
Step 1: Calculate the Mean
For a binomial distribution, the expected value (mean) is calculated using the formula:
μ=n⋅p
where:
n=82 (the number of trials),
p=0.39 (the probability of success).
Substituting the values:
μ=82⋅0.39=31.98
Step 2: Calculate the Variance
The variance of a binomial distribution is given by the formula:
σ2=n⋅p⋅q
where q=1−p. Thus, we have:
q=1−0.39=0.61
Now substituting the values into the variance formula:
σ2=82⋅0.39⋅0.61=19.508
Step 3: Calculate the Standard Deviation
The standard deviation is the square root of the variance:
σ=n⋅p⋅q=19.508≈4.417
Final Answer
The expected value (mean) for the number of successes in this binomial distribution is: