Math Problem Statement
Solution
Let's walk through the problem step-by-step.
Problem Analysis:
We are dealing with a binomial distribution, where:
- is the number of trials (the total number of eyeglasses examined),
- is the probability of success (in this case, the probability that an eyeglass is defective),
- The mean (expected value) for a binomial distribution is given by:
Solution:
(a) Find the parameters and :
- (since 18 eyeglasses were examined)
- (15.6% defective rate expressed as a decimal)
So:
(b) Find the mean number of defective eyeglasses: Using the formula for the mean:
So, the mean number of defective eyeglasses is:
Summary:
- Mean
Would you like me to explain further or answer anything else?
Here are 5 related questions to explore next:
- What is the variance formula for a binomial distribution?
- How do you calculate the probability of exactly 2 defective eyeglasses?
- What is the standard deviation of the defective eyeglasses in this case?
- How does increasing impact the mean and variance?
- How would you determine the probability of at least 3 defective eyeglasses?
Tip: Always convert percentages to decimals before using them in statistical formulas to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Binomial Distribution
Probability
Mean (Expected Value)
Formulas
Mean (μ) = n × p
Theorems
Binomial Distribution Theorem
Suitable Grade Level
Grades 10-12
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