Question 1

Fifty-one percent of workers are confident that they will retire with a comfortable lifestyle. You randomly select 10 workers, ask them if they are confident with their life after retirement. What is the probability that at least three of them say yes. Round the answer to 4 decimal places.

Question 2 (4 points)

Rolling a 6-side die 5 times, what is the probability of obtaining exact three 2s? Round the answer to three decimal places.

Question 3 (4 points)

A test consists of 25 multiple choice questions, and each question has 5 answers, where only one of them is the correctanswer. Let X be the number of questions answered correctly by random guessing. Which of the following statements are true?

Question 3 options:

	The range of the probability distribution is 25.
	The expected value of X is 5.
	The variance of the probability distribution is 2.
	The mean of the probability distribution is 5.
	The standard deviation of the probability distribution is 4.

The expected value of X is 5.

The variance of the probability distribution is 2.

The mean of the probability distribution is 5.

The standard deviation of the probability distribution is 4.

Question 4: Which of the following random variables follows a binomial distribution?

Question 4 options:

A test contains 5 true/false questions and 5 multiple choice questions, where each question has 5 selections. Answering all questions by random guessing, and let x be the number of correct answers obtained.

Rolling a die 6 times, let x be the number of prime numbers observed.

Tossing a coin, let x be the number of times needed to get a head for the first time.

A bag contains only red and green marbles. Drawing a marble at random from the bag with replacement 5 times, and let x be the number of red marbles obtained.

A bag contains only red and green marbles. Drawing a marble at random from the bag without replacement 7 times, and let x be the number of green marbles obtained.

Question 5

Fifty-one percent of workers are confident that they will retire with a comfortable lifestyle. You randomly select 10 workers, ask them if they are confident with their life after retirement. What is the probability that at least three of them say yes. Round the answer to 4 decimal places.