Assume that a procedure yields a binomial distribution with a trial repeated n=30 times. Use the binomial probability formula to find the probability of x=5 successes given the probability p=1/5 of success on a single trial. Round to three decimal places.
A) 0.172
B) 0.067
C) 0.198
D) 0.421

Question

Assume that a procedure yields a binomial distribution with a trial repeated  n=30  times. Use the binomial probability formula to find the probability of  x=5  successes given the probability  p=1/5  of success on a single trial. Round to three decimal places.
A)  0.172 
B)  0.067 
C)  0.198 
D)  0.421

Quizplus · Accepted Answer

The binomial probability formula is $P(X = k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single trial, and $\binom{n}{k}$ is the binomial coefficient. Plugging in $n=30$, $k=5$, and $p=1/5$, we get $P(X = 5) = \binom{30}{5}(1/5)^5(4/5)^{25}$. Calculating this gives approximately 0.172.

Assume That a Procedure Yields a Binomial Distribution with a Trial