78% of college graduates say they spent two years or less at their first full-time job after graduating college. you randomly select 10 college graduates and ask each how long they stayed at their first full-time job after graduating college. find the probability that out of 10 college graduates, spend less that two years at their first job. is it less than 6, at least 6, exactly 6
To answer this question, we need to determine the probability of each case separately: less than 6 college graduates spending less than two years on their first job, at least 6 college graduates spending less than two years on their first job, and exactly 6 college graduates spending less than two years on their first job.
First, let's calculate the probability of a single college graduate spending less than two years on their first job. Given that 78% of college graduates fall into this category, the probability is 0.78.
To find the probability of less than 6 college graduates spending less than two years on their first job, we need to calculate the probability of each possibility. This can be determined using the binomial probability formula.
P(X < 6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
Where X is the number of college graduates spending less than two years on their first job, and P(X=k) represents the probability of exactly k college graduates falling into this category.
Using the formula, we can calculate each individual probability and then sum them up to find P(X < 6).
Next, let's determine the probability of at least 6 college graduates spending less than two years on their first job. This can be found by subtracting P(X < 6) from 1.
P(X >= 6) = 1 - P(X < 6)
Finally, to find the probability of exactly 6 college graduates spending less than two years on their first job, we can use the binomial probability formula again.
P(X = 6) = (10 choose 6) * 0.78^6 * (1-0.78)^(10-6)
Where (10 choose 6) represents the number of ways to choose 6 college graduates out of 10, and 0.78^6 * (1-0.78)^(10-6) represents the probability of getting exactly 6 college graduates out of 10 who spend less than two years on their first job.
By following these steps, we can determine the probabilities for each case.