Approximately 10.3% Of American High School Students Drop Out Before Graduation. Choose 10 Students Entering High School At Random. Find the probability that at least 6 will graduate
Find P(6), P(7), P(8), P(9), and P(10).
The easiest way to do this would be to use a binomial probability function table.
Find each value, then add together for your probability.
Approimately 10.3% of American high school students drop out of school before gradution. Choose 10 students entering high school at random. Find the probability that (Assume binomial distribution): a. Exactly two drop out b. At least 7 graduate c. All ten stay in school and graduate
Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
To find the probability that at least 6 out of 10 randomly chosen students will graduate, we can use the binomial probability formula.
The formula for binomial probability is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Where:
- P(x) is the probability of getting exactly x successes.
- n is the total number of trials (which is 10 in this case, as we have 10 students).
- x is the number of successes we are interested in (at least 6 in this case).
- p is the probability of success (which is the probability of a student graduating, so 1 - dropout rate = 1 - 0.103 = 0.897).
- (nCx) represents "n choose x", which calculates the number of ways to choose x items from a set of n items.
Now, we need to find the probability of at least 6 students graduating, which means finding the probability of 6, 7, 8, 9, or 10 students graduating.
We can calculate this probability by summing the individual probabilities for each case:
P(at least 6) = P(6) + P(7) + P(8) + P(9) + P(10)
P(6) = (10C6) * (0.897)^6 * (0.103)^(10-6)
P(7) = (10C7) * (0.897)^7 * (0.103)^(10-7)
P(8) = (10C8) * (0.897)^8 * (0.103)^(10-8)
P(9) = (10C9) * (0.897)^9 * (0.103)^(10-9)
P(10) = (10C10) * (0.897)^10 * (0.103)^0
To calculate these probabilities, we need to find the binomial coefficients (nCx), which represent the number of combinations. The formula for binomial coefficients is:
nCx = n! / (x! * (n-x)!)
Using this formula, we can calculate the individual probabilities and then sum them to find the final probability of at least 6 students graduating.