Binomial Mean and Standard Deviation Example  Summary and Q&A
TL;DR
Calculate the mean and standard deviation for the number of peas with green pods in groups of 26.
Key Insights
 🙊 Hybridization experiments with peas can be analyzed using binomial distributions.
 ✖️ The mean of a binomial distribution is calculated by multiplying the sample size by the probability of success.
 The standard deviation of a binomial distribution is obtained by taking the square root of the product of the sample size, the probability of success, and the probability of failure.
 ⏳ The range rule of thumb can be used to determine significantly low or high values by subtracting or adding 2 times the standard deviation from the mean, respectively.
Transcript
assume that hybridization experiments are conducted with peas having the property that for offspring there is a point two five probability that the pea has green pods and assume that the offspring peas are randomly selected in groups of 26 okay so P is going to be 0.25 that's our probability of success success here is a pea that has a green pod oka... Read More
Questions & Answers
Q: What is the formula for calculating the mean or expected value of a binomial distribution?
The formula is NP, where N is the sample size and P is the probability of success. In this case, N is 26 and P is 0.25, resulting in a mean of 6.5.
Q: What is the formula for calculating the standard deviation of a binomial distribution?
The formula is the square root of N times P times Q, where Q is 1 minus P. Plugging in the values N = 26, P = 0.25, and Q = 0.75, the standard deviation is 2.2.
Q: How can the range rule of thumb be used to find significantly low or high values?
The minimum usual value is calculated by subtracting 2 times the standard deviation from the mean. In this case, the minimum usual value is 6.5  2*(2.2) = 2.1. The maximum usual value is calculated by adding 2 times the standard deviation to the mean, resulting in 6.5 + 2*(2.2) = 10.9.
Q: Is the result of one pea with green pods significantly low?
Yes, the result of one pea with green pods is significantly low because it is less than the minimum usual value of 2.1.
Summary & Key Takeaways

A hybridization experiment is conducted with peas, where there is a 0.25 probability of a pea having green pods.

The mean number of peas with green pods in groups of 26 is 6.5.

The standard deviation for the number of peas with green pods is 2.2.