Answer:
P= 0.0606 = 60.6%
Step-by-step explanation:
Binomial Distribution
The required probability will be calculated by using the Binomial Distribution with n=385 independent events each with a probability of success equal to p=0.0362 with k=8 or fewer successes.
The PMF (Probability Mass Function) for the Binomial Distribution is
[tex]\displaystyle B(k,n,p)=\binom{n}{k}p^kq^{n-k}[/tex]
Where
[tex]q = 1-p=0.9638[/tex]
We need to compute a range of probabilities from k=8 to k=0. We'll show how to compute for k=8
[tex]\displaystyle B(8,385,0.0362)=\binom{385}{8}0.0362^8\ 0.9638^{377}=0.03014[/tex]
When the probability is cumulative and a high number of calculations need to be performed, we use automated tools (like Excel, digital calculator, etc) to compute the sum. We used Excel's BINOMDIST(8, 385, 0.0362, 1) function to get the total probability to get
[tex]\boxed{P=0.0606 = 60.6\%}[/tex]
