X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.
A) $P ( X = 4 ) = 0.13824$
B) $P ( X = 4 ) = 0.4$
C) $P ( X = 4 ) = 0.16667$
D) $P ( X = 4 ) = 0.06144$
E) $P ( X = 4 ) = 0.69984$

Question

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.  
A) $P ( X = 4 ) = 0.13824$
B) $P ( X = 4 ) = 0.4$
C) $P ( X = 4 ) = 0.16667$
D) $P ( X = 4 ) = 0.06144$
E) $P ( X = 4 ) = 0.69984$

Quizplus · Accepted Answer

The probability $P(X = 4)$ in a binomial distribution is calculated using the formula $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$, where $n$ is the number of trials, $p$ is the probability of success on a single trial, and $k$ is the number of successes. Plugging in $n = 6$, $p = 0.4$, and $k = 4$, we get $P(X = 4) = \binom{6}{4} (0.4)^4 (0.6)^2 = 15 \times 0.0256 \times 0.36 = 0.13824$.

X Is a Binomial Variable With n=6n = 6n=6 And p=0.4p = 0.4p=0.4

X Is a Binomial Variable With $n = 6$ And $p = 0.4$