Consider a binomial distribution with 8 trials. Look at a binomial probability d

Question

Consider a binomial distribution with 8 trials. Look at a binomial probability distribution table showing binomial probabilities for various values of p, the probability of success on a single trial. (a) For what value of p is the distribution symmetric? = .5 What is the expected value of this distribution? Is the distribution centered over the value? Yes No (b) For small values of p, is the distribution skewed right or left? O right O left (c) For large values of p, is the distribution skewed right or left? O right O left

Explanation / Answer

Given that, For binomial distribution,

sample size = n = 8

probability of success = p

A )The shape of a binomial distribution is symmetrical

when p=0.5 or for large n

B ) The expected value is

E(X) = n*p = 8 * 0.5 = 4

yes the distribution is centered over the value

C ) For small p and small n the binomial distribution is skewed to right.

option A ) Right is correct

D ) For large p and small n the binomial distribution is skewed to left

option B ) Left is correct

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