Math Problem Statement
- What is the expected value of the binomial distributions where n = 16 and P=0.85? a) 6 b) 7.4 c) 12.4 d)13.6
Solution
The expected value of a binomial distribution is given by the formula:
where is the number of trials, and is the probability of success on each trial.
Given:
Plugging these values into the formula:
Therefore, the expected value is 13.6, which corresponds to option:
d) 13.6
Would you like more details on this calculation, or do you have any questions?
Here are 5 related questions for further exploration:
- What is the variance of this binomial distribution?
- How do you calculate the standard deviation of a binomial distribution?
- What is the probability of getting exactly 13 successes in this distribution?
- How does changing the probability affect the expected value of a binomial distribution?
- What is the probability of getting at least 14 successes in this distribution?
Tip: Remember that for binomial distributions, the expected value indicates the average number of successes expected over a large number of trials.
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Binomial Distribution
Formulas
Expected value of a binomial distribution: E(X) = n * P
Theorems
-
Suitable Grade Level
High School
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