Review of Chapter 8 and 9 - Cabarrus County Schools



Review of Chapter 8 and 9 Name__________________

|Conditions for Binomial |Conditions for Geometric |

|Independent events |Independent events |

|Probability of success is equal for every trial |Probability of success is equal for every trial |

|Two possible outcomes |Two possible outcomes |

|Fixed number of trials (X = # of “successes”) |Fixed number of successes, one (X = # of trials to get one |

| |success |

Binomial formula: [pic]

Binomial pdf is for set number of successes; binomial cdf is for the chance that you get x number of success or less!

[pic] [pic] *You can use normal approximation if [pic] and

Geometric formula (not shown on sheet): [pic]

[pic]

[pic] [pic]

A parameter is a measurement of _____________________; a statistic is a measurement of ________________.

Fill in the correct notation: sample mean ____; population mean ___; sample proportion ___; population proportion ___; sample standard deviation ___; population standard deviation ___.

Sampling proportions: [pic] [pic]

Two rules of thumb: to use standard deviation formula, the population must be at least 10 times the sample size.

AND

To assume normal approximation, [pic] and

Sample means: [pic] [pic]

To use standard deviation formula, the population must be at least 10 times the sample.

1. Each child born to a particular set of parents has a probability of 0.25 of having blood type O. If these parents have 5 children, what is the probability that exactly 2 of them have type O blood?

2. A university claims that 80% of its basketball players graduate. A random sample of 20 players found that only 10 graduated. If the university’s claim is really true, then what is the probability that 10 or fewer players from a sample of 20 will graduate?

3. A test for the presence of antibodies to the AIDS virus in blood has probability 0.99 of detecting the antibodies when they are present. Suppose that during a year, 20 units of blood with AIDS antibodies pass through a blood bank.

a. What is the probability that all 20 units are detected as contaminated?

b. What is the mean number of units (out of 20) that will be detected?

4. A computer testing program is designed to present questions to the user until a correct answer is given. Suppose that each question has five possible answers, and that the user is guessing.

a. What is the probability that the user will have to answer 5 questions in order to get one question correct?

b. What is the probability that the user will have to answer more than 4 questions to get one correct?

5. In some cultures, it is very important to have a son to carry on the family name. Suppose that a couple plans to have children until they have exactly one son, and that the probability that any child will be male is 0.5.

a. What is the probability that the couple will have exactly one child?

b. What is the probability that the couple will have at least 3 children?

c. How many children should the couple expect to have?

6. Voter registration records show that 68% of all voters in Indianapolis are registered as Republicans. To test whether the numbers dialed by a random digit dialing device really are random, you use the device to call 150 randomly chosen residential telephones in Indianapolis. Of the registered voters contacted, 73% are registered Republicans.

a. Is each boldface number a parameter or a statistic? Give the appropriate notation for each.

b. What are the mean and the standard deviation of the sample proportion of registered Republicans in samples of size 150 from Indianapolis?

c. Find the probability of obtaining an SRS of size 150 from the population of Indianapolis voters in which 73% or more are registered Republicans. How well is your random digit device working?

7. Sulfur compounds such as dimethyl sulfide (DMS) are sometimes present in wine. DMS causes “off-odors” in wine, so winemakers want to know the odor threshold, the lowest concentration of DMS that the human nose can detect. Different people have different thresholds, so we start by asking about the DMS thresholds in the population of all adults. Extensive studies have found that the DMS odor threshold of adults follows roughly a normal distribution with mean [pic] micrograms per liter and standard deviation [pic] micrograms per liter.

In an experiment, we present tasters with both natural wine and the same wine spiked with DMS at different concentrations to find the lowest concentration at which they identify the spiked wine. Here are the odor thresholds (measured in micrograms of DMS per liter of wine) for 10 randomly chosen subjects.

28 40 28 33 20 31 29 27 17 21

The mean threshold for these subjects is x-bar = 27.4. Find the probability of getting a sample mean even farther away from [pic] than x-bar = 27.4.

8. The Wechsler Adult Intelligence Scale (WAIS) is a common “IQ Test” for adults. The distribution of WAIS scores for persons over 16 ears of age is approximately normal with mean 100 and standard deviation 15.

a. What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?

b. What are the mean and standard deviation of the sampling distribution of the average WAIS score x-bar for an SRS of 60 people?

c. What is the probability that the average WAIS score of an SRS of 60 people is 105 or higher?

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[pic]

[pic]

Note: Sample means tend to be more normal than individual distributions. You can assume a normal distribution if the n ≥ 30 (CLT).

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