1. A psychologist studied the number of puzzles subjects were able to solve in a five minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution:
X 1 2 3 4
Probability 0.20 0.40 0.30 0.10Find the following:P(X < 3) = AnswerP(X ≤ 3) = AnswerP(X = 2.5) = Answer11-The probability distribution below is for the random variable X = the number of classes for which full time students at a university are enrolled in an academic term.No. of classes, X 4 5 6 7
Probability 0.2 0.5 0.2 0.1Calculate the expected value of X. Be sure to show your work.12-Write a sentence or two interpreting the expected value in the context of the questionAnswer:13-A department supervisor will be purchasing one of two similar photocopy machines, A or B. Machine A costs $10,000. Machine B costs $10,500. This department replaces photocopy machines every three years. The repair contract for machine A costs $50 per month and covers an unlimited number of repairs.Answer the following:1. Over the next three years, how much will the supervisor pay overall, for both the purchase and the repair contract, if she chooses photocopy machine A? Show your work.
2. The repair contract for machine B costs $200 per repair. Based on past performance, the distribution of the number of repairs needed over any one-year period for machine B is shown below.
Number of repairs 0 1 2 3
Probability 0.50 0.25 0.15 0.10
3. Calculate how much should the supervisor should expect to pay overall for the next three years, for both the purchase and repairs, if she chooses machine B? Use expected values, and show your work.
4. Which machine will be more cost effective for the supervisor's department over the next three years, machine A or machine B?Answer: