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
The probability that a bus will arrive late at the civic center is. 35, and the probability that it will be on time or early in. 60. Explain why the statement is incorrect.
To find the probability that fewer than 6 out of 10 college graduates spend less than two years at their first job, we can use the binomial probability formula.
The formula for the probability of getting exactly k successes in n trials is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes,
C(n, k) is the number of ways to choose k successes from n trials (n choose k),
p is the probability of success in one trial, and
n is the total number of trials.
In this case, out of the college graduates surveyed, the probability of spending less than two years at their first job is given as 78%, which translates to a probability of success (p) of 0.78. Therefore, the probability of spending more than two years at their first job is (1 - 0.78) = 0.22.
Let's calculate the probabilities:
1. Probability of less than 6 college graduates spending less than two years at their first job (k < 6):
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
2. Probability of at least 6 college graduates spending less than two years at their first job (k ≥ 6):
P(X ≥ 6) = 1 - P(X < 6)
3. Probability of exactly 6 college graduates spending less than two years at their first job (k = 6):
P(X = 6) = C(10, 6) * (0.78)^6 * (0.22)^4
Let's calculate the probabilities step by step:
1. Probability of less than 6 college graduates spending less than two years at their first job (k < 6):
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= C(10, 0) * (0.78)^0 * (0.22)^10 + C(10, 1) * (0.78)^1 * (0.22)^9 + C(10, 2) * (0.78)^2 * (0.22)^8 + C(10, 3) * (0.78)^3 * (0.22)^7 + C(10, 4) * (0.78)^4 * (0.22)^6 + C(10, 5) * (0.78)^5 * (0.22)^5
2. Probability of at least 6 college graduates spending less than two years at their first job (k ≥ 6):
P(X ≥ 6) = 1 - P(X < 6)
3. Probability of exactly 6 college graduates spending less than two years at their first job (k = 6):
P(X = 6) = C(10, 6) * (0.78)^6 * (0.22)^4
Now, you can calculate these probabilities using the given formulas.