AP Stats FRQ Test Questions with
complete solution
1999 #1 Commercial Aircraft - correct answer ✔A) Yes, a line is an
appropriate model for this data, because the residuals are evenly and
randomly scattered both above and below the residual line.
B) The slope of the least squares regression line is 233.517. This means that
the number of commercial aircraft flying in the United States each year
increases by 233.517.
C) The value of the y-intercept is 2939.93. This means that in 1990, (the
starting year) the number of commercial aircraft flying in the United States
was 2939.93.
D) The predicted number of commercial aircraft flying in 1992 is 3406.964.
E) The actual number of commercial aircraft flying in 1992 was 3447.
2003 #2 Class Action Lawsuits - correct answer ✔A) The parameter of
interest is the proportion of people in the population who have experienced a
defect in the particular make and model of this car.
B) Ho : 5 % of the cars of this make and model have the defect
Ha : More than 5 % of cars of this make and model have the defect
C) A type ll error in this situation is concluding that 5 % of cars of this make
and model have the defect, when really more than 5 % of cars of this make
and model have the defect. A type l error in this situation would be to conclude
that more than 5 % of cars of this make and model have the defect, when
really only 5 % have the defect.
2003B #2 Age vs. Income - correct answer ✔A) The probability that a person
chosen at random from those sample will be 31-45 age category is 89/207=
0.43.
, B) The probability that a person chosen at random from those in the sample
whose incomes are over $50,000 will be in the 31-45 age category is 35/96=
0.36458.
C) Based on my answers from (a) and (b), annual income is not independent
of age in the category from the sample.
2004 #3 Brontosaurs - correct answer ✔A) The probability of X is not
binomial because the probability of choosing a male femur is not the same
each time, because they were selected without replacement, so the probability
changes of choosing a male femur decreases each time.
B) The probability that all 4 femurs are male is 0.0433
C) Based on this result and my answer to (b), I do not believe that males and
females were equally represented, because the probability of choosing all 4
malles seemed too small to not be significant.
D) It is not reasonable to generalize the population based on my conclusion to
©, because the sampled is biased. The 20 brontosaur skeletons were all
found clustered in the same area, so the random sample of 4 is not randomly
selected from the population, leading to possible bias.
2004B #3 Bauxite Cars - correct answer ✔A) normalcdf(70.7,1E99,70,.9) =
0.2183. The probability that the weight of ore in a randomly selected car will
be 70.7 pounds or more is 0.2183.
B) If the weight of a randomly selected car was 70.7 pounds, we would not
suspect that the mechanism is overfilling the cars. 70.7 is less than 1 standard
deviation away from the mean, so it is a plausible weight value, and we would
not conclude that the mechanism is overfilling the cars.
C) If the filling equipment is functioning properly, the probability that the mean
weight of ore in 10 randomly selected cars will be 70.7 pounds or more is
0.0069.
D) If the sample mean is 0.7 pounds off from the population mean, we would
suspect that the mechanism is definitely overfilling the cars, because the
sample and the population should have the same mean.
complete solution
1999 #1 Commercial Aircraft - correct answer ✔A) Yes, a line is an
appropriate model for this data, because the residuals are evenly and
randomly scattered both above and below the residual line.
B) The slope of the least squares regression line is 233.517. This means that
the number of commercial aircraft flying in the United States each year
increases by 233.517.
C) The value of the y-intercept is 2939.93. This means that in 1990, (the
starting year) the number of commercial aircraft flying in the United States
was 2939.93.
D) The predicted number of commercial aircraft flying in 1992 is 3406.964.
E) The actual number of commercial aircraft flying in 1992 was 3447.
2003 #2 Class Action Lawsuits - correct answer ✔A) The parameter of
interest is the proportion of people in the population who have experienced a
defect in the particular make and model of this car.
B) Ho : 5 % of the cars of this make and model have the defect
Ha : More than 5 % of cars of this make and model have the defect
C) A type ll error in this situation is concluding that 5 % of cars of this make
and model have the defect, when really more than 5 % of cars of this make
and model have the defect. A type l error in this situation would be to conclude
that more than 5 % of cars of this make and model have the defect, when
really only 5 % have the defect.
2003B #2 Age vs. Income - correct answer ✔A) The probability that a person
chosen at random from those sample will be 31-45 age category is 89/207=
0.43.
, B) The probability that a person chosen at random from those in the sample
whose incomes are over $50,000 will be in the 31-45 age category is 35/96=
0.36458.
C) Based on my answers from (a) and (b), annual income is not independent
of age in the category from the sample.
2004 #3 Brontosaurs - correct answer ✔A) The probability of X is not
binomial because the probability of choosing a male femur is not the same
each time, because they were selected without replacement, so the probability
changes of choosing a male femur decreases each time.
B) The probability that all 4 femurs are male is 0.0433
C) Based on this result and my answer to (b), I do not believe that males and
females were equally represented, because the probability of choosing all 4
malles seemed too small to not be significant.
D) It is not reasonable to generalize the population based on my conclusion to
©, because the sampled is biased. The 20 brontosaur skeletons were all
found clustered in the same area, so the random sample of 4 is not randomly
selected from the population, leading to possible bias.
2004B #3 Bauxite Cars - correct answer ✔A) normalcdf(70.7,1E99,70,.9) =
0.2183. The probability that the weight of ore in a randomly selected car will
be 70.7 pounds or more is 0.2183.
B) If the weight of a randomly selected car was 70.7 pounds, we would not
suspect that the mechanism is overfilling the cars. 70.7 is less than 1 standard
deviation away from the mean, so it is a plausible weight value, and we would
not conclude that the mechanism is overfilling the cars.
C) If the filling equipment is functioning properly, the probability that the mean
weight of ore in 10 randomly selected cars will be 70.7 pounds or more is
0.0069.
D) If the sample mean is 0.7 pounds off from the population mean, we would
suspect that the mechanism is definitely overfilling the cars, because the
sample and the population should have the same mean.
