Probability & Statistics Exam 2

Probability & Statistics Exam 2

Round final answers to the fourth and write as a probability (decimal) unless otherwise stated.

Problem 1

1. You have the opportunity to play two games. Create a probability distribution (table) and compute the expected value for each game. Round to the second.

o Game 1: A spin on the roulette wheel with a $70 bet on the number 15 and $150 bet on red for one spin of the roulette wheel. (Recall: A Roulette wheel has 38 numbers with 18 black, 18 red and 2 green. The colors are equally spaced from each other. If you place your money on the correct color (Black or Red), you win the equivalent of your bet (even money). If you place your money on a specific number you win 35 times your bet. If you do not land on your bet (color or number) you lose your money. (6 pts)

o Game 2: You roll a regular six-sided die and win 4 times whatever number you rolled. The game costs $7 to play. (6 pts)

Which game would you choose to play and why? (3 pts)

2. Suppose a life insurance company sells a one year, $450,000 term life insurance policy to a 55-year-old man for $380. The probability the man dies during the year is 0.00067. Create a probability distribution for this problem then find and interpret the expected value of this policy for the insurance company. (10 pts)

Problem 2

The Centers for Disease Control and Prevention reported that diastolic blood pressures (in mmHg) of adult women in the United States are approximately normally distributed with a mean of 85 and a standard deviation of 6. Be sure to include the calculator commands and a graph of the situation for each part below.

A. What blood pressure represents the bottom 38% of blood pressures? (4 pts)

 

 

B. What proportion of women have blood pressures that are more than 93? (4 pts)

 

 

 

C. Would it be unusual for a blood pressure to be more extreme than 66? Find the probability and z-score and explain using both. (9 pts)

Probability: _____________

z-score: _________________________________________________________________________________

_______________________________________________________________________________________

D. What two blood pressure measurements hold the middle 48% of women’s blood pressures? (4 pts

E. Doctors only want to warn women about their blood pressure if it is unusually high. At what blood pressure measurement would doctors start to warn their patients (when is it unusually high)? (4 pts)

Probability & Statistics Exam 2

Problem 3

An industrial machine is known to produce defective components at a 12% rate. We are interested in the number defective components. Round to the fourth for all parts.

1. A sample of 4 components is taken. A. Create the probability distribution. (5 pts)

B. Find the mean and standard deviation. Interpret the mean using the word expect. (4 pts)

Mean = ____________________ Standard deviation:________________________

Interpretation: _________________________________________________________________

_____________________________________________________________________________

2. If a sample of 14 components is taken (use the same probability of success as above). (4 pts each)

A. Find the probability that at least 8 parts will be defective (show calculator commands).

B. Find the probability that at most 6 parts will be defective (show calculator commands).

C. Find the probability more than 3 parts will be defective (show calculator commands).

D. Find the probability that fewer than 6 parts will be defective (show calculator commands).

Problem 4

These problems are not related to any previous problems and are separate from each other.

A. Would it be unusual for a data value to be more extreme than 2.68 standard deviations from the mean? Find the probability and explain by z score and probability. (Draw a picture and show calc commands) (7 pts)

B. Would it be unusual for a data value to be more extreme than – 1.35 standard deviations from the mean? Find the probability and explain by z score and probability. (Draw a picture and show calc commands) (7 pts)

C. For 24 trials that follow a binomial distribution with the probability of failure at 23%, find the probability of exactly 11 successes. (Use your calculator to do this, not by hand, and show your calc commands) (4 pts)

D. Find the grade in our class for the following student and show your work. (7 pts)

Exams = 80%, Homework = 10%, Quizzes = 5%, Classwork/Discussions = 5% AND your lowest exam score gets dropped

Exam 1 :90 Exam 2: 87 Exam 3: 59 Exam 4: 68 Final Exam: 86 Homework: 78

Quizzes: 72 Classwork/Discussions: 98

Probability & Statistics Exam 2

• Create a probability distribution and compute expected value for Game 1 and Game 2.,

• Choose which game to play and explain why.,

• Create a probability distribution for the life insurance policy and find the expected value.,

• For a normal distribution (mean = 85, SD = 6), find blood pressure representing the bottom 38%.,

• For a binomial distribution with p = 0.12, find the probability that at least 8 of 14 parts are defective.