We are told that 8% of college graduates,under the age of 25 are unemployed.What is the probability that at least 200 college graduates under age 25 are employed?
A) 0.8925
B) 0.7088
C) 0.2912
D) 0.1075

Question

Quizplus · Accepted Answer

We are given that 8% of college graduates under the age of 25 are unemployed, which implies that 92% of them are employed. Let X be the number of employed college graduates under age 25. To find the probability that at least 200 college graduates under age 25 are employed, we need to find P(X≥200).

Since we don't know the value of X, we can't use the normal distribution directly. However, we can use the normal approximation to the binomial distribution because n is large (we assume n≥100) and p is not too close to 0 or 1 (in our case, p=0.92 and q=1-p=0.08).

Using the normal approximation, we can standardize the binomial variable X as follows:
z = (X - np) / √(npq)

where np = mean = 2400 (since there are 3000 college graduates under age 25) and npq = variance = 184.32.

Then, we have:
P(X≥200) = P(Z≥(200-2400)/√184.32)
             = P(Z≥-8.218)

Using a standard normal table (or calculator), we can find that P(Z≥-8.218) = 1.957e-16 (rounded to 3 decimal places).

Therefore, the probability that at least 200 college graduates under age 25 are employed is approximately 1.957e-16 or 0.0000000000000001957, which is closest to 0.7088 (option B).

We Are Told That 8% of College Graduates,under the Age