To explain: The approximation of a binomial distribution as a
A binomial distribution with parameters
Given:A binomial distribution with parameters number of trials as n and probability of success as p.
Explanation:A binomial distribution with large sample of trials n, can be assumed to be a normal distribution to calculate the respective probabilities. Calculating the cumulative probabilities for large sample of trails n will be very tedious so approximation to a normal distribution would help. To assume a binomial distribution as a normal distribution the following conditions are to be met
If the above conditions are satisfied then a binomial distribution with parameters
Thus for large sample of trails n which satisfy the given conditions, a binomial distribution can be approximated as a normal distribution to calculate its respective probabilities.
Plot:The binomial histogram for
Interpretation:For large sample of trials
The binomial histogram is symmetric and proper bell-shaped curve. Thus the distribution can be approximated as a normal distribution.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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