AP Statistics Probability Questions and Answers (frequently asked Questions) | Already
Passed
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. ** Answ** 2019 FRQ #3
The probability that a person selected will be someone whose response is never and who is a
woman. ** Answ** 0.0636
The probability that a person selected will be someone whose response is never or who is a
woman. ** Answ** 0.5864
The probability that a person selected will be someone whose response is never given that person
is a woman ** Answ** 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. ** Answ** 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. ** Answ** 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. ** Answ** 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. ** Answ** 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? ** Answ** 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? ** Answ** ($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. ** Answ** 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. **
Answ**
Passed
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. ** Answ** 2019 FRQ #3
The probability that a person selected will be someone whose response is never and who is a
woman. ** Answ** 0.0636
The probability that a person selected will be someone whose response is never or who is a
woman. ** Answ** 0.5864
The probability that a person selected will be someone whose response is never given that person
is a woman ** Answ** 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. ** Answ** 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. ** Answ** 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. ** Answ** 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. ** Answ** 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? ** Answ** 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? ** Answ** ($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. ** Answ** 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. **
Answ**
