AP Stats Inference

A friend has placed a large number of plastic disks in a hat and invited you to select one at random.  He informs you that half are red and half are blue.  If you draw a disk, record the color, replace it, and repeat 100 times, which of the following is true?

• It is unlikely you will choose red more than 50 times.

• If you draw 10 blue disks in a row, it is more likely you will draw a red on the next try.

• The overall proportion of red disks drawn should be close to 0.50.

• The chance that the 100th draw will be red depends on the results of the first 99 draws.

A dealer in Las Vegas selects 10 cards from a standard deck of 52 cards.  Let Y be the number of diamonds in the 10 cards selected.  Which of the following best describes this setting?

• Y has a binomial distribution with n = 10 observations and probability of success p = 0.25.

• Y has a binomial distribution with n = 10 observations and probability of success p = 0.25, provided the deck is shuffled well.

• Y is a binomial distribution with n = 10 observations and probability of success p = 0.25, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

• Y has a geometric distribution with n = 10 observations and probability of success p = 0.25

It is known that about 90% of the widgets made by Buckley Industries meet specifications.  Every hour a sample of 18 widgets is selected at random for testing and the number of widgets that meet specifications is recorded.  What is the approximate mean and standard deviation of the number of widgets meeting

• μ = 1.62; σ = 1.414

• μ = 1.62; σ = 1.265

• μ = 16.2; σ = 1.62

• μ = 16.2; σ = 1.273

Le the random variable X represent the amount of money Carl makes tutoring statistics students in the summer.  Assume that X is Normal with mean $240 and standard deviation $60.  The probability is approximately 0.6 that, in a randomly selected summer, Carl will make less than about

• $144

• $216

• $255

• $30

The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes.  What is the probability that a random sample of 40 students will have a mean completion time greater than 25 minutes?

• 0.9678

• 0.0322

• 0.0344

• 0.3851

A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times.  The probability that more than 1/3 of the tosses are heads is closest to 

• 0.9951

• 0.33

• 0.109

• 0.09

The incomes in a certain large population of college teachers have a normal distribution with mean $60,000 and standard deviation $5000.  Four teachers are selected at random from this population to serve on a salary review committee.  What is the probability that their average salary exceeds $65,000?

• 0.0228

• 0.1587

• 0.8413

• 0.9772

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population.  Which of the following would produce a wider confidence interval, based on these same data?

• Use a larger confidence level

• Use a smaller confidence level

• Use the same confidence level, but compute the interval n times.  Approximately 5% of these intervals will be larger

• Increase the sample size

You are told that the proportion of those who answered "yes" to a poll about internet use is 0.70, and that the standard error is 0.0459.  The sample size is

• 50

• 99

• 100

• 200

The standardized test scores of 16 students have mean x̄ = 200 and standard deviation s = 20.  What is the standard error of x̄?

• 20

• 10

• 5

• 1.25