Answer:
Explanation:
To find the probability that at least 260 out of 800 randomly selected incoming first-year students have elected to enroll in the personal finance course, we can use the binomial probability formula.
The formula for the probability of x successes in n trials, where the probability of success in each trial is p, is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
In this case, n = 800 (the number of trials or students), p = 0.30 (the probability of success or the proportion of students who elect to enroll in the course), and we want to find the probability of at least 260 students, so we need to find the sum of probabilities for x = 260 to 800.
Calculating the probability for each value of x and summing them up can be quite laborious. However, we can use the complement rule to simplify the calculation. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
So, the probability of at least 260 students electing to enroll in the course is equal to 1 minus the probability of fewer than 260 students electing to enroll.
Now let's calculate the probability of fewer than 260 students electing to enroll in the course.
P(fewer than 260) = P(0) + P(1) + P(2) + ... + P(259)
To find these probabilities, we can use a binomial probability calculator or a statistical software package.
Once we have the probability of fewer than 260 students electing to enroll, we can subtract it from 1 to find the probability of at least 260 students electing to enroll in the course.
Remember to double-check your calculations using a reliable binomial probability calculator or a statistical software package to ensure accuracy.
In summary, to find the probability that at least 260 out of 800 randomly selected incoming first-year students have elected to enroll in the personal finance course, you need to calculate the probability of fewer than 260 students electing to enroll using the binomial probability formula and subtract it from 1.