Asked by Arteria Jones on Jun 15, 2024
Verified
Let X be a binomial random variable with n = 25 and p = 0.01.
a.Use the binomial table to find P(X = 0),P(X = 1),and P(X = 2).
b.Find the variance and standard deviation of X.
Binomial Random Variable
A type of random variable that takes fixed values with probabilities defined by a binomial distribution, usually representing the number of successes in a series of trials.
Standard Deviation
An index quantifying the spread or variability among a collection of numbers, illustrating the distance of values from their average.
- Attain an understanding of binomial distribution principles, including computing probabilities, expected values, variance, and standard deviation.
- Learn how to utilize statistical tables for solving problems related to binomial and Poisson distributions.
Verified Answer
KG
Kshama GuptaJun 19, 2024
Final Answer :
a. P(X = 0)= 0.7778,P(X = 1)= 0.1964,and P(X = 2)= 0.0238
b. σ2 = np(1 − p)= 25(0.01)(0.99)= 0.2475 and σ = 0.4975
b. σ2 = np(1 − p)= 25(0.01)(0.99)= 0.2475 and σ = 0.4975
Learning Objectives
- Attain an understanding of binomial distribution principles, including computing probabilities, expected values, variance, and standard deviation.
- Learn how to utilize statistical tables for solving problems related to binomial and Poisson distributions.