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

n = 200

p = 0.15

q = 1 - p = 0.85

To find P(X=27):

Applying Continuity Correction:
To find P(26.5 < X < 27.5):

For X = 26.5:

Z = (26.5 - 30)/5.0498

= - 0.6931

By Technology, Cumulative Area Under Standard Normal Curve = 0.2441

For X = 27.5:

Z = (27.5 - 30)/5.0498

= - 0.4951

By Technology, Cumulative Area Under Standard Normal Curve = 0.3103

So,

P(X=27) = 0.3103 - 0.2441

          = 0.0662

So,

Answer is:

0.0662