Exam 8: Probability: the Mathematics of Chance

If a fair die is rolled once, what is the probability of getting a number less than five?

The Olympic flag consists of five intertwined circles, one in each of the colors black, blue, green, red, and yellow. What is the probability that a random coloring of the five circles using these colors will produce the exact match of the Olympic symbol?

The scores of students on a standardized test are Normally distributed with a mean of 300 and a standard deviation of 40. Using the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean, find the probability that a randomly chosen student scores below 273.2 on the test.

Two dice are rolled and the sum is recorded. What sis the most likely outcome?

A computer system requires users to have an access code that consists of a three-digit number that is not allowed to start with zero and cannot repeat digits. How many such codes are possible?

Using the central limit theorem for a Normally distributed variable, how would the standard deviation of the sample means for samples of size 200 be related to that of samples of size 3200?

A spinner numbered 1 through 10 is spun and one die is tossed simultaneously. The number spun and the number rolled are recorded. How many outcomes are in the sample space?

A computer is programmed to randomly print two letters in a row without repeating a letter. What is the probability that the first combination printed is the word "DO"?

Use the following information to answer the Questions: A company gives a new screening test to test its employees for tuberculosis (TB). The results are summarized in the following table. Test result Has TB Does not have TB Positive 21 14 Negative 4 140 -If an employee is randomly selected from the company, what is the probability that the employee has TB?

The batteries used by a calculator have useful lives that follow a Normal distribution, with an average life of 2000 hours and a standard deviation of 200 hours. In the production process, the manufacturer draws random samples of 100 batteries and determines the mean useful life of the sample. What is the standard deviation _x of this mean?

Three dice are rolled and the number rolled on each die is recorded. The outcomes in the sample space are all equally likely.

The scores of students on a standardized test form a Normal distribution with a mean of 300 and a standard deviation of 40. Using the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean, find the lower and upper quartile scores for this test.

A game consists of tossing three coins. Find the probability model for the number of coins showing heads.

A continuous probability model has a constant density curve on the range 0 to 12. What is the height of the density curve?

The scores of students on a standardized test are Normally distributed with a mean of 300 and a standard deviation of 40. Between what two values do 99.7% of the test scores lie?

Use the following to answer the questions: You roll two dice and record the sum shown. The sample space is the set of all possible sums, which are 2, 3, . . . , 11, 12. -What other outcome has a probability equal to the probability of "the sum is 2"?

The annual income of residents in a county is $42,000 with a standard deviation of $10,000. Under the assumption that the distribution of annual incomes is Normal, between what two values do 95% of the incomes of county residents lie?

Find the probability of drawing a three or a heart from a regular (bridge) deck of cards. (Such a deck consists of four suits of 13 cards each. The suits are hearts, spades, diamonds, and clubs. The cards are 1 through 10, Jack, Queen, and King.)

We need to create serial numbers that start with one of the letters a, b, c, d, or f followed by three nonrepeating digits. How many serial numbers can be created?

A spinner numbered 1 through 10 is spun and one die is rolled simultaneously. The sum of the number spun and the number rolled is recorded. How many outcomes are in the sample space?