Question

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=55​,
x=33​,
p=0.55
p(3)=_________

Answer 1

Answer:

P(33) = 0.0826

Step-by-step explanation:

The binomial distribution in this case has parameters n=55 and p=0.55.

The probability that k successes happen with these parameters can be calculated as:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}$

We have to calculate the probability fo X=33 succesess.

This can be calculated using the formula above as:

$P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826$