Exam 8: Probability: the Mathematics of Chance

According to the central limit theorem, how does the standard deviation of averages over four observations compare with the standard deviation of individual observations?

The weight of potato chip bags filled by a machine at a packaging plant is Normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh less than 14.6 ounces?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Between what two measurements will 95% of all diameters of ball bearings be found?

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 a positive test result?

We need to create three-digit code numbers that must begin with a 7. How many such codes can be made?

The marketing department of an electronics manufacturer has done research on the number of television sets owned by families in a large town. The probability model for the number of sets owned by a randomly chosen family is given below. What is the mean number of sets per family? Number of 0 1 2 3 sets Probability 0.04 0.34 0.47 0.15

A pair of fair dice is rolled and the sum of the faces showing is recorded. What is the probability of getting a sum greater than 9?

The shelf life of a battery produced by one major company is known to be Normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What is the upper quartile of battery shelf life? Use the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean.

For a sample space {1,2,3,4,5,6,7,8}, two events are defined as follows: Event A: A chosen number is greater than 4 Event B: A chosen number is a prime number; that is, 2, 3, 5, or 7 Are those events A and B dependent or independent?

Use the following information to solve the Questions: A random number generator is modeled by a uniform probability model with a density curve that has height 1/10 between 0 and 10 and height 0 everywhere else. -For this model, what is $P ( 0 \leq X \leq 1 ) ?$

The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution of study times is Normal, what percent of students study between 22.9 and 25.7 hours?

Suppose a game has three outcomes, A, B, and C with probabilities P(A) = 0.2, P(B) = 0.3, and P(C) = 0.5. A player will receive $3 when outcome A occurs, $4 when outcome B occurs, and will have to pay $2 when outcome C occurs. What is the mean value of one trial of the game?

A game consists of rolling a regular die. You pay $5 to play the game, and the $5 is not returned. If you roll a 1 or 2, you win $6. If you roll a 3, 4, 5, or 6, you win nothing. What is the mean value for this game, taking into account the $5 cost of the game?

A game consists of tossing a coin and rolling a six-sided die. The results can be recorded easily; for example, if heads shows on the coin and a 4 shows on the die, you can record this as H4. List the sample space for the results of this game.

A sample space consists of three outcomes, X, Y, and Z. Which of the following could be a legitimate assignment of probabilities to the outcomes?

A die is rolled and a coin is flipped simultaneously. The number rolled on the die and whether the coin lands heads or tails is recorded. How many outcomes are in the sample space?

How many possible ways are there for drawing three spades from a regular (bridge) deck of cards?

Three dice are tossed. The number rolled on each die is recorded. How many outcomes are in the sample space?

Suppose a trial consists of rolling two dice and reporting the smaller of the two numbers rolled. What are the possible outcomes? Are they equally likely?

A spinner with regions numbered 1 to 4 is spun and a coin is tossed. Both the region number and heads or tails is recorded. Write the sample space.