AP Stats Random Variables

Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given below. The equation of the least-squares regression line is

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Describe the correlation in the graph shown.

• Strong Negative

• Strong Positive

• Weak Negative

• Weak Positive

What letter do we use to represent correlation coefficient?

• c

• r

• p

• h

• This residual graph represents a linear fit.
• This graph represents a nonlinear fit.
• This residual graph represents no fit.

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

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 die is loaded so that the number 6 comes p three times as often as any other number.  What is the probability of rolling a 4, 5, or 6?

• 2/3

• 1/2

• 5/8

• 1/3

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