2. In a certain state, it has been shown that only 56% of the high school graduates who are capable of college work actually enroll in colleges.Find the probability that, among the 11 capable high school graduates in this state, each number will enroll in college.
c.At least 4
d. Exactly 2
e. Less than 3
f. none
f None
I don't understand. 0nly 11 capable students in the state???
.56 (11) = 6.16
I have no idea what the standard deviation is so can not do more. If I knew it I would use mean of 6.16 and some standard deviation in:
http://davidmlane.com/hyperstat/z_table.html
Yes, I wondered about this state's educational achievements as well :)
WHAT IS THE ANSWER
To find the probability for each scenario, we need to calculate the probability of each event happening and then multiply them together.
First, let's calculate the probability of a single high school graduate enrolling in college. Given that only 56% of capable high school graduates enroll, the probability of a single graduate enrolling is 0.56.
Now, let's solve each scenario:
c. At least 4 high school graduates enroll in college:
To calculate this probability, we need to consider all possible combinations where 4, 5, 6, 7, 8, 9, 10, or 11 graduates enroll. The probability of each individual combination occurring is 0.56 raised to the number of graduates enrolling, multiplied by 0.44 raised to the number of graduates not enrolling. Then, we sum up the probabilities for all these combinations. The formula for the probability of at least 4 people enrolling can be expressed as:
P(at least 4 enrolling) = P(4 enrolling) + P(5 enrolling) + ... + P(11 enrolling)
To calculate this, we can use a binomial probability distribution or a calculator to evaluate this summation.
d. Exactly 2 high school graduates enroll in college:
To calculate this probability, we need to consider the combination when exactly 2 people enroll. The formula for this probability can be expressed as:
P(exactly 2 enrolling) = P(2 enrolling) = C(11, 2) * 0.56^2 * 0.44^9
where C(n, r) represents the combination formula (n choose r).
e. Less than 3 high school graduates enroll in college:
To calculate this probability, we need to consider the combination when 0 or 1 person enrolls. The formula for this probability can be expressed as:
P(less than 3 enrolling) = P(0 enrolling) + P(1 enrolling) = P(0 enrolling) + C(11, 1) * 0.56^1 * 0.44^10
where P(0 enrolling) means the probability that no one enrolls.
Given the information provided, we cannot determine P(0 enrolling), and therefore, we cannot calculate the probability for this scenario.
f. None of the high school graduates enroll in college:
Given the information provided, we cannot determine the probability of none of the high school graduates enrolling in college.