AP Statistics Probability FRQs Exam
Questions With Already Solved
Correctly Answers | 2025
A medical researcher surveyed a large group of men and women about whether they
take medicine as prescribed. The responses were categorized as never, sometimes, or
always. The relative frequency of each category is shown in the table. CORRECT
ANSWERS 2019 FRQ #3
The probability that a person selected will be someone whose response is never and
who is a woman. CORRECT ANSWERS 0.0636
The probability that a person selected will be someone whose response is never or who
is a woman. CORRECT ANSWERS 0.5864
The probability that a person selected will be someone whose response is never given
that person is a woman CORRECT ANSWERS 0.12
For the people surveyed, are the events of being a person whose response is never and
being a woman independent? Justify your answer. CORRECT ANSWERS Yes, the
event of being a person who responds never is independent of the event of being a
woman because P P (never | woman) (never) 0.12.
Assume that, in a large population, the probability that a person will always take
medicine as prescribed is 0.54. If 5 people are selected at random from the population,
what is the probability that at least 4 of the people selected will always take medicine as
prescribed? Support your answer. CORRECT ANSWERS Define X as the number of
people in a random sample of five people who always take their medicine as prescribed.
Then X has a binomial distribution with n = 5 and p = 0.54, and 5 5 41 50 P( 4) = (0.54)
(0.46) (0.54) (0.46) 0.19557 + 0.04592 0.24149.
A company that manufactures smartphones developed a new battery that has a longer
life span than that of a traditional battery. From the date of purchase of a smartphone,
the distribution of the life span of the new battery is approximately normal with mean 30
months and standard deviation 8 months. For the price of $50, the company offers a
two-year warranty on the new battery for customers who purchase a smartphone. The
warranty guarantees that the smartphone will be replaced at no cost to the customer if
the battery no longer works within 24 months from the date of purchase. CORRECT
ANSWERS 2019 FRQ #5
In how many months from the date of purchase is it expected that 25 percent of the
batteries will no longer work? Justify your answer. CORRECT ANSWERS The 25th
percentile of the standard normal distribution is −0.6745. Consequently the 25th
, percentile of a normal distribution with mean 30 months and standard deviation 8
months is 30 8( 0.6745) 24.6 +− = months.
Suppose one customer who purchases the warranty is selected at random. What is the
probability that the customer selected will require a replacement within 24 months from
the date of purchase because the battery no longer works? CORRECT ANSWERS The
probability that a randomly selected customer will need to request a replacement
because the battery fails within 24 months from the date of purchase is ( ) 24 30 (life
span 24 months) ( 0.75) 0.2266.
The company has a gain of $50 for each customer who purchases a warranty but does
not require a replacement. The company has a loss (negative gain) of $150 for each
customer who purchases a warranty and does require a replacement. What is the
expected value of the gain for the company for each warranty purchased? CORRECT
ANSWERS ($50) (life span 24 months) ( $150) (life span 24 months) ($50) (0.7734)
( $150) (0.2266) $4.68.
A machine at a manufacturing company is programmed to fill shampoo bottles such that
the amount of shampoo in each bottle is normally distributed with mean 0.60 liter and
standard deviation 0.04 liter. Let the random variable A represent the amount of
shampoo, in liters, that is inserted into a bottle by the filling machine. CORRECT
ANSWERS 2022 FRQ #3 Part 1
A bottle is considered to be underfilled if it has less than 0.50 liter of shampoo.
Determine the probability that a randomly selected bottle of shampoo will be underfilled.
Show your work. CORRECT ANSWERS
After the bottles are filled, they are placed in boxes of 10 bottles per box. After the
bottles are placed in the boxes, several boxes are placed in a crate for shipping to a
beauty supply warehouse. The manufacturing company's contract with the beauty
supply warehouse states that one box will be randomly selected from a crate. If 2 or
more bottles in the selected box are underfilled, the entire crate will be rejected and sent
back to the manufacturing company. CORRECT ANSWERS 2022 FRQ #3 Part 2
The beauty supply warehouse manager is interested in the probability that a crate
shipped to the warehouse will be rejected. Assume that the amounts of shampoo in the
bottles are independent of each other. CORRECT ANSWERS
Define the random variable of interest for the warehouse manager and state how the
random variable is distributed. CORRECT ANSWERS
Determine the probability that a crate will be rejected by the warehouse manager. Show
your work. CORRECT ANSWERS
To reduce the number of crates rejected by the beauty supply warehouse manager, the
manufacturing company is considering adjusting the programming of the filling machine
Questions With Already Solved
Correctly Answers | 2025
A medical researcher surveyed a large group of men and women about whether they
take medicine as prescribed. The responses were categorized as never, sometimes, or
always. The relative frequency of each category is shown in the table. CORRECT
ANSWERS 2019 FRQ #3
The probability that a person selected will be someone whose response is never and
who is a woman. CORRECT ANSWERS 0.0636
The probability that a person selected will be someone whose response is never or who
is a woman. CORRECT ANSWERS 0.5864
The probability that a person selected will be someone whose response is never given
that person is a woman CORRECT ANSWERS 0.12
For the people surveyed, are the events of being a person whose response is never and
being a woman independent? Justify your answer. CORRECT ANSWERS Yes, the
event of being a person who responds never is independent of the event of being a
woman because P P (never | woman) (never) 0.12.
Assume that, in a large population, the probability that a person will always take
medicine as prescribed is 0.54. If 5 people are selected at random from the population,
what is the probability that at least 4 of the people selected will always take medicine as
prescribed? Support your answer. CORRECT ANSWERS Define X as the number of
people in a random sample of five people who always take their medicine as prescribed.
Then X has a binomial distribution with n = 5 and p = 0.54, and 5 5 41 50 P( 4) = (0.54)
(0.46) (0.54) (0.46) 0.19557 + 0.04592 0.24149.
A company that manufactures smartphones developed a new battery that has a longer
life span than that of a traditional battery. From the date of purchase of a smartphone,
the distribution of the life span of the new battery is approximately normal with mean 30
months and standard deviation 8 months. For the price of $50, the company offers a
two-year warranty on the new battery for customers who purchase a smartphone. The
warranty guarantees that the smartphone will be replaced at no cost to the customer if
the battery no longer works within 24 months from the date of purchase. CORRECT
ANSWERS 2019 FRQ #5
In how many months from the date of purchase is it expected that 25 percent of the
batteries will no longer work? Justify your answer. CORRECT ANSWERS The 25th
percentile of the standard normal distribution is −0.6745. Consequently the 25th
, percentile of a normal distribution with mean 30 months and standard deviation 8
months is 30 8( 0.6745) 24.6 +− = months.
Suppose one customer who purchases the warranty is selected at random. What is the
probability that the customer selected will require a replacement within 24 months from
the date of purchase because the battery no longer works? CORRECT ANSWERS The
probability that a randomly selected customer will need to request a replacement
because the battery fails within 24 months from the date of purchase is ( ) 24 30 (life
span 24 months) ( 0.75) 0.2266.
The company has a gain of $50 for each customer who purchases a warranty but does
not require a replacement. The company has a loss (negative gain) of $150 for each
customer who purchases a warranty and does require a replacement. What is the
expected value of the gain for the company for each warranty purchased? CORRECT
ANSWERS ($50) (life span 24 months) ( $150) (life span 24 months) ($50) (0.7734)
( $150) (0.2266) $4.68.
A machine at a manufacturing company is programmed to fill shampoo bottles such that
the amount of shampoo in each bottle is normally distributed with mean 0.60 liter and
standard deviation 0.04 liter. Let the random variable A represent the amount of
shampoo, in liters, that is inserted into a bottle by the filling machine. CORRECT
ANSWERS 2022 FRQ #3 Part 1
A bottle is considered to be underfilled if it has less than 0.50 liter of shampoo.
Determine the probability that a randomly selected bottle of shampoo will be underfilled.
Show your work. CORRECT ANSWERS
After the bottles are filled, they are placed in boxes of 10 bottles per box. After the
bottles are placed in the boxes, several boxes are placed in a crate for shipping to a
beauty supply warehouse. The manufacturing company's contract with the beauty
supply warehouse states that one box will be randomly selected from a crate. If 2 or
more bottles in the selected box are underfilled, the entire crate will be rejected and sent
back to the manufacturing company. CORRECT ANSWERS 2022 FRQ #3 Part 2
The beauty supply warehouse manager is interested in the probability that a crate
shipped to the warehouse will be rejected. Assume that the amounts of shampoo in the
bottles are independent of each other. CORRECT ANSWERS
Define the random variable of interest for the warehouse manager and state how the
random variable is distributed. CORRECT ANSWERS
Determine the probability that a crate will be rejected by the warehouse manager. Show
your work. CORRECT ANSWERS
To reduce the number of crates rejected by the beauty supply warehouse manager, the
manufacturing company is considering adjusting the programming of the filling machine
