Answer :
Final answer:
The probability that more than 65% of a sample of 50 students will support Mr. X can be calculated using the binomial distribution. By summing up the probabilities for all percentages greater than 65%, we can find the final probability.
Explanation:
To find the probability that more than 65% of a sample of 50 students will support Mr. X, we can use the binomial distribution. The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.
In this case, the probability of success is 80% (the proportion of the population that supports Mr. X), and we have 50 trials (the sample size). We want to find the probability of getting more than 65% successes.
Using the binomial distribution formula, we can calculate the probability as follows:
- Calculate the probability of getting exactly 65% successes: P(X = 65) = (50 choose 65) * (0.8^65) * (0.2^(50-65))
- Calculate the probability of getting exactly 66% successes: P(X = 66) = (50 choose 66) * (0.8^66) * (0.2^(50-66))
- Continue this process for each percentage from 65% to 100%.
- Sum up the probabilities for all percentages greater than 65% to find the final probability.
By performing these calculations, we can find the probability that more than 65% of a sample of 50 students will support Mr. X.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ14