Math Problem Statement

  1. 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 E(X)E(X) of a binomial distribution is given by the formula:

E(X)=n×PE(X) = n \times P

where nn is the number of trials, and PP is the probability of success on each trial.

Given:

  • n=16n = 16
  • P=0.85P = 0.85

Plugging these values into the formula:

E(X)=16×0.85=13.6E(X) = 16 \times 0.85 = 13.6

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:

  1. What is the variance of this binomial distribution?
  2. How do you calculate the standard deviation of a binomial distribution?
  3. What is the probability of getting exactly 13 successes in this distribution?
  4. How does changing the probability PP affect the expected value of a binomial distribution?
  5. 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

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Suitable Grade Level

High School