Question

1. A student takes a 12 question multiple choice test. There are 5 answer choices, and the student guesses on all the questions. What is the probability the student will get exactly 7 questions correct in order to pass? Round to 5 decimal places.

a. 0.00332

b. 0.00587

c. 0.08304

d. 0.00213

2. If the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 5 defective parts from a sample of 100? (Round answer to four places.) *

a. 0.0500

b. 0.0900

c. 0.1800

d. 0.5000

3. On a test to obtain a securities license there are 20 questions with possible answers A, B, C, D, & E. Getting 70% (or 14 out of 20) correct is necessary to pass. A student is certain he knows 10 but must guess on the other 10. What is the probability of getting at least 4 correct by guessing on the 10? *

a. 0.0328

b. 0.1209

c. 0.8791

d. 0.9672

Answer 1

1. Student have to answer 12 question. Hence number of trials n=12
2. Each question has 5 options with only one correct answer and all other incorrect answers. Student is equally likely to pick any outcome in any given question. Hence, probability of choosing correct answer is 1/5 = 0.20. Probability of choosing incorrect answer is 1–1/5 = 4/5 = 0.80
3. Total number of success is exactly 7 and failure is 5 amongst the 12 questions.

Clearly it is following binomial distribution with parameters n=12 and p=.20
Then probability of getting 7 ans corret is
(option a)

(2) Let X be the random variable denoting the number of defective parts
Total number of sample n=100 or number of trials n=100
probability of getting defective part is given as p=.05

Clearly, X follows binomial distribution with parameter n=100 and p=.05
Then probability of getting exactly 5 defective part out of 100 is
( option c)

(3) We have to find probability of getting at least 4 correct by guessing on the 10.
Let X be the random variable denoting the number of correct answer.
Number of questions n=10 or number of trials n=100
Each question has 5 options with only one correct answer and all other incorrect answers. Student is equally likely to pick any outcome in any given question. Hence, probability of choosing correct answer is 1/5 = 0.20. Probability of choosing incorrect answer is 1–1/5 = 4/5 = 0.80

Clearly, X follows binomial distribution with parameter n=10 and p=.20
Then probability of getting at least 4 correct by guessing on the 10.

(option b)