Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-$$\frac { 1 } { 3 }$$ n = 10, x = 2, p =
A)0.1951
B)0.1929
C)0.2156
D)0.0028

Question

Quizplus · Accepted Answer

The procedure results in a binomial distribution because it involves a fixed number of trials (n = 10), each trial has only two possible outcomes (success or failure), the probability of success (p) is constant ($\frac{1}{3}$), and the trials are independent. The correct probability for x = 2 successes can be calculated using the binomial probability formula: $$P(X = x) = \binom{n}{x}p^x(1-p)^{n-x}$$ Substituting n = 10, x = 2, and p = $\frac{1}{3}$ gives the probability of approximately 0.1951, making option A correct.

Determine Whether the Given Procedure Results in a Binomial Distribution 13\frac { 1 } { 3 }31​

Determine Whether the Given Procedure Results in a Binomial Distribution $\frac { 1 } { 3 }$