A sc tourists bureau survey showed that 75 % of those who seek information about the state actually come to visit . The office received 8 requests for information. What is the probability that probability that 4 to 6 inclusive of the people will visit sc?
To find the probability that 4 to 6 inclusive people will visit South Carolina (SC), we need to use the concept of probability and the information provided in the survey.
First, let's determine the total number of people who are likely to visit SC based on the survey. The survey states that 75% of those who seek information about the state actually come to visit. Therefore, the probability of a person visiting SC after seeking information is 0.75.
Next, let's calculate the probability that a specific number of people will visit SC. We can use the binomial probability formula for this:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
Where:
- P(x) is the probability of x people visiting SC
- n is the total number of requests for information received by the office (8 in this case)
- x is the number of people visiting SC (4, 5, or 6 in this case)
- p is the probability of a person visiting SC after seeking information (0.75)
- (nCx) is the combination formula, which calculates the number of ways to choose x items out of n.
Now, let's calculate the probabilities for each case and sum them up to get the desired probability:
P(4) = (8C4) * (0.75^4) * (0.25^4) = (8! / (4! * (8-4)!)) * (0.75^4) * (0.25^4)
P(5) = (8C5) * (0.75^5) * (0.25^3) = (8! / (5! * (8-5)!)) * (0.75^5) * (0.25^3)
P(6) = (8C6) * (0.75^6) * (0.25^2) = (8! / (6! * (8-6)!)) * (0.75^6) * (0.25^2)
Finally, we can sum up these individual probabilities to get the final answer:
P(4 to 6 inclusive) = P(4) + P(5) + P(6)
You can use a calculator or software with statistical functions to calculate these probabilities accurately.