AP Stats Chapter 6

In the wild, 400 randomly selected blooming azalea plants are observed and classified according to flower petal color (white, pink, or orange) and whether or not they have a fragrance. The table gives the results. If a single azalea plant is selected at random, which one of the following is the probability that it has pink flower petals or no fragrance?

• 0.04

• 0.635

• 0.595

• 0.555

In the wild, 400 randomly selected blooming azalea plants are observed and classified according to flower petal color (white, pink, or orange) and whether or not they have a fragrance. The table gives the results. Suppose a single azalea plant is chosen at random. Which of the following expressions establishes that the events “Fragrance” and “Pink” are not independent?

• 
• 
• 

In a large city, 82% of residents own a cell phone. Suppose that we randomly select three city residents. What is the probability that at least one of the three residents does not own a cell phone? [The city is large enough so that we can assume independence].

• 0.994

• 0.449

• 0.006

• 0.551

A jar contains 10 red marbles and 15 blue marbles. If you randomly draw two marbles from the jar (without replacement), what is the probability that they are the same color?

• 0.5

• 0.15

• 0.52

• 0.48

8% of the customers entering Irby's Books will make a purchase. What  is the probability that the next 3 customers will each make a purchase, assuming purchases are independent of each other?

• 0.000512

• 0.24

• 24

• .064

8% of the customers entering Irby's Books will make a purchase. What  is the probability that at least 1 of the next 10 customers will make a purchase, assuming purchases are independent of each other?

• 0.566

• 0.44

• .92

• 0.8

If the last four digits of a phone number are chosen by a random number generator, which number is more likely to occur:  2873 or 9999?

• 2873

• 9999

• neither

• both

A game consists of drawing three cards at random from a deck of 52 playing cards. You win 3 points for each red card that is drawn. It costs 2 points each time you play. For one play of this game, the sample space S for the net number of points you gain (after deducting the cost of play) is

• S = {-2, 1, 4, 7}

• S = {0, 1, 2, 3}

• S = {0, 3, 6, 9}

• S = {-2, 3, 6, 9}

You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. “Least-squares” refers to

• Minimizing the sum of the squares of the 25 houses’ heating costs.

• Minimizing the sum of the squares of the number of rooms in each of the 25 houses.

• Minimizing the sum of the products of each house’s actual heating costs and the predicted heating cost based on the regression equation.

• Minimizing the sum of the squares of the difference between each house’s heating costs and number of rooms.

• Minimizing the sum of the squares of the residuals.

Leonardo da Vinci, the renowned painter, speculated that an ideal human would have an armspan (distance from the outstretched fingertip of the left hand to the outstretched fingertip of the right hand) that was equal to his height. Is it possible to predict armspan from height? The following computer regression printout shows the results of a least-squares regression of armspan on height, both in inches, for a sample of 18 high school students.

The students’ armspans ranged from 62 to 76 inches. Which of the following statements is true? (click on the picture to enlarge)

• If one of the students in the sample had a height of 70 inches and an armspan of 68 inches, then the residual for this student would be about –2.36 inches.

• The correlation between height and armspan is .871.

• Contrary to da Vinci’s speculation, the regression model suggests that, for these students at least, height is about 84% of armspan.

• For every one-inch increase in armspan, the regression model predicts about a 0.84-inch increase in height.

• For a student 66 inches tall, this model would predict an armspan of about 68 inches.