Question

According to national data, about 15% of American college students earn a graduate degree. Using this estimate, what is the probability that exactly 27 undergraduates in a random sample of 200 students will earn a college degree? Hint: Use the normal approximation to the binomial distribution, where p = 0.15 and q = 0.85. (Round your answer to four decimal places.)

Answer 1

Using the binomial probability relation, the probability that exactly 27 graduates earn a college degree is 0.069

Using the relation :

P(x = x) = nCx * p^x * q^(n-x)

• Probability of success, p = 0.15
• q = 1 - p = 1 - 0.15 = 0.85
• Number of trials, n = 200
• X = 27

Probability of exactly 27 graduates can be defined thus :

P(x = 27) = 200C27 × 0.15^27 × 0.85^173

P(x = 27) = 0.0686264

Therefore, the probability of selecting exactly 27 graduates is 0.069

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