Question

According to national data, about 13% of American college students earn a graduate degree. Using this estimate, what is the probability that exactly 28 undergraduates in a random sample of 200 students will earn a college degree? Hint: Use the normal approximation to the binomial distribution, where

p = 0.13

and

q = 0.87.

(Round your answer to four decimal places

Answer 1

Solution

Given that ,

p = 0.13

1 - p = 1 - 0.13 = 0.87

n = 200

x = 28

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 28) = ((200! / 28! (200 - 28)!) * 0.13²⁸ * (0.87)^{200 - 28}

=  ((200! / 28! (172)!) * 0.13²⁸ * (0.87)¹⁷²

= 0.0743

Probability = 0.0743