Question

A professor gives a test with 100 true-false questions. If 60 or more are necessary to pass, what is the probability that a student will pass by random guessing?

Answer 1

Here's one way to do this problem; there may be others. Using the normal approximation to the binomial distribution, we have the following:

p = .5
q = .5 --> q = 1 - p
x = 60
n = 100

We now need to find mean and standard deviation.
mean = np = (100)(.5) = 50
standard deviation = √npq = √(100)(.5)(.5) = √(25) = 5

Using z-scores:
z = (x - mean)/sd
z = (60 - 50)/5 = 2

Use a normal distribution table to find the probability. If the table shows from mean to z, check from mean to z = 2.00. Then take the value you find in the table and subtract it from .5000 for your probability.

I hope this will help.