Question

9. There are 50 true-or-false questions on an exam. For each question there is only one correct answer. If you need to get at least 65% of the questions correct to pass the test, what is the probability of passing this test by making random guesses?

10. Referring to the previous problem, find the mean (expected value) and variance for the number of questions you answer correctly by making random guess.

Answer 1

9) Given that

number of question n =50

65% at least questions correct to pass the test = 32.5

p =0.5

Pr(X≥32)=0.016+0.0087+0.0044+0.002+0.0008+0.0003+0.0001+0+0+0+0+0+0+0+0+0+0+0+0

= 0.0325

which means that the probability we are looking for is Pr(X≥32)=0.0325.

10)

The parameters provided for the Binomial Distribution are:

n=50,p=0.5

The population mean is computed as:

μ=n⋅p=50⋅0.5=25

Also, the population variance is obtained using the following formula

σ2=n⋅p⋅(1−p)=50⋅0.5⋅0.5=12.5