AP Statistics Chapter 5 Review

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital’s capacity will be exceeded?

• 0.011

• 0.965

• 0.035

• 0.989

• 0.092

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

• n = 10, p = 0.5

• n = 40, p = 0.88

• n = 100, p = 0.2

• n = 100, p = 0.99

• n = 1000, p = 0.003

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean = 10 ounces and standard deviation  = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

• Normal, with mean 10 ounces and standard deviation 1 ounce.

• Normal, with mean 40 ounces and standard deviation 2 ounces

• Normal, with mean 40 ounces and standard deviation 4 ounces

• binomial, with mean 40 ounces and standard deviation 2 ounces

• binomial, with mean 40 ounces and standard deviation 4 ounces.

Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?

• X = student’s height; Y = student’s weight

• X = student’s IQ; Y = student’s GPA

• X = student’s PSAT Math score; Y = student’s PSAT Verbal score

• X = average amount of homework the student does per night; Y = student’s GPA

• X = average amount of homework the student does per night; Y = student’s height

A 90% confidence interval for p, the proportion of all high school students at a local high school who participate in after school activities was found to be (0.743, 0.896). Which of the following is correct?

• About 90% of the high school students have between 74.3% to 89.6% chance of participating in after school activities.

• There is a 90% probability that the sample proportion lies between 0.743 to 0.896.

• We are reasonably certain the true proportion of all high school students who participate in after school activities is between 74.3% to 89.6%.

• If a second sample was taken, there is a 90% chance that its confidence interval would contain 0.75.

• This confidence interval indicates than 75% of high school students participate in after school activities.

A 90% confidence interval for p, the proportion of all high school students at a local high school who participate in after school activities was found to be (0.743, 0.896). Which of the following would be true about a 95% confidence interval constructed using the same data? I. The interval would be wider because the critical z* would be larger. II. The interval would be narrower because the critical z* would be smaller. III. The interval would be wider because the standard error would be larger.

• I only

• II only

• III only

• I and III only

• I and II only

You are going to create a 95% confidence interval for a population proportion and want the margin of error to be no more than 0.05. Historical data indicate that the population proportion has remained constant at about 0.7. What is the minimum size random sample you need to construct this interval?

• 385

• 322

• 274

• 275

• 323

A researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% confidence interval, a 99% confidence interval will be…

• It would be narrower because it omits only 1% of the possible samples instead of 5%

• It would be wider because it has a higher confidence, which requires a larger margin of error.

• It would be narrower because it has a higher confidence, which requires a larger margin of error.

• It would be the same because the sample is the same.

• You can’t tell because the margin of error varies from sample to sample.

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that…

• 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

• The percent of the population who jog is certain to between 15% and 21%.

• 95% of the population jog between 15% and 21% of the time.

• We can be 95% confident that the sample proportion is captured by the confidence interval.

• If Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is…

• 190

• 27.84

• 22.73

• 16.07

• 13.13