Question

According to national data, about 14% of American college students earn a graduate degree. Using this estimate, what is the probability that exactly 30 undergraduates in a random sample of 200 students will earn a college degree? Hint: Use the normal approximation to the binomial distribution, where

p = 0.14

and

q = 0.86.

(Round your answer to four decimal places.)

Answer 1

The sample Size n = 200

The proportion of American college students earn a graduate degree is p = 0.14

Let X be the number of American college students earn a graduate degree

X ~Binomial(200,0.14)

Since sample size is very large, we can use normal approximation to binomial, if the condions are satisfied.

The conditions are np>5 and nq> 5

np = 200*0.14 =25 >5

nq =200*0.86 =172>5

Since both conditions are satisfied, normal approximateion is appropriate

The Mean is

The standard deviation