MATH 225N WEEK 6 2026 COMPREHENSIVE
ASSESSMENT SCRIPT SOLVED QUESTIONS
ANSWERS UPDATED REVIEW SET
◉ Suppose a basketball player is an excellent free throw shooter and
makes 91% of his free throws (i.e., he has a 91% chance of making a
single free throw). Assume that free throw shots are independent of
one another. Suppose this player gets to shoot four free throws. Find
the probability that he misses all four consecutive free throws.
Round to the nearest ten-thousandth.
Answer: 0.0001
◉ Provide an appropriate response.
A single die is rolled twice. The set of 36 equally likely outcomes is
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3,
3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of
getting two numbers whose sum is less than 13..
Answer: 1
◉ The complement of 4 heads in the toss of 4 coins is.
Answer: at least one tail.
,◉ How many distinct arrangements can be formed from all the
letters of "students"?.
Answer: 10,080
◉ A human gene carries a certain disease from the mother to the
child with a probability rate of 57%. That is, there is a 57% chance
that the child becomes infected with the disease. Suppose a female
carrier of the gene has four children. Assume that the infections of
the four children are independent of one another. Find the
probability that at least one of the children get the disease from
their mother. Round to the nearest thousandth..
Answer: 0.966
◉ In a carnival game, a person wagers $2 on the roll of two dice. If
the total of the two dice is 2, 3, 4, 5, or 6 then the person gets $4 (the
$2 wager and $2 winnings). If the total of the two dice is 8, 9, 10, 11,
or 12 then the person gets nothing (loses $2). If the total of the two
dice is 7, the person gets $0.75 back (loses $0.25). What is the
expected value of playing the game once?.
Answer: $-0.04
◉ Provide an appropriate response.
,The produce manager at a farmer's market was interested in
determining how many oranges a person buys when they buy
oranges. He asked the cashiers over a weekend to count how many
oranges a person bought when they bought oranges and record this
number for analysis at a later time. The data is given below in the
table. The random variable x represents the number of oranges
purchased and P(x) represents the probability that a customer will
buy x apples. Determine the mean number of oranges purchased by
a customer..
Answer: 3.97
◉ Provide an appropriate response.
The sum of the probabilities of a discrete probability distribution
must be.
Answer: equal to one
◉ A lab orders a shipment of 100 rats a week, 52 weeks a year, from
a rat supplier for experiments that the lab conducts. Prices for each
weekly shipment of rats follow the distribution below:
How much should the lab budget for next year's rat orders assuming
this distribution does not change. (Hint: find the expected price.).
Answer: $637.00
, ◉ Consider the discrete probability distribution to the right when
answering the following question. Find the probability that x
exceeds 4..
Answer: 0.48
◉ Consider the discrete probability distribution to the right when
answering the following question. Find the probability that x equals
4..
Answer: 0.27
◉ A random variable is.
Answer: a numerical measure of the outcome of a probability
experiment.
◉ Assume that the random variable X is normally distributed, with
mean and standard deviation Compute the probability P(57 < X <
105)..
Answer: 0.8914
◉ The amount of corn chips dispensed into a 32-ounce bag by the
dispensing machine has been identified as possessing a normal
distribution with a mean of 32.5 ounces and a standard deviation of
0.2 ounce. What chip amount represents the 67th percentile for the
bag weight distribution? Round to the nearest hundredth..
Answer: 32.59
ASSESSMENT SCRIPT SOLVED QUESTIONS
ANSWERS UPDATED REVIEW SET
◉ Suppose a basketball player is an excellent free throw shooter and
makes 91% of his free throws (i.e., he has a 91% chance of making a
single free throw). Assume that free throw shots are independent of
one another. Suppose this player gets to shoot four free throws. Find
the probability that he misses all four consecutive free throws.
Round to the nearest ten-thousandth.
Answer: 0.0001
◉ Provide an appropriate response.
A single die is rolled twice. The set of 36 equally likely outcomes is
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3,
3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of
getting two numbers whose sum is less than 13..
Answer: 1
◉ The complement of 4 heads in the toss of 4 coins is.
Answer: at least one tail.
,◉ How many distinct arrangements can be formed from all the
letters of "students"?.
Answer: 10,080
◉ A human gene carries a certain disease from the mother to the
child with a probability rate of 57%. That is, there is a 57% chance
that the child becomes infected with the disease. Suppose a female
carrier of the gene has four children. Assume that the infections of
the four children are independent of one another. Find the
probability that at least one of the children get the disease from
their mother. Round to the nearest thousandth..
Answer: 0.966
◉ In a carnival game, a person wagers $2 on the roll of two dice. If
the total of the two dice is 2, 3, 4, 5, or 6 then the person gets $4 (the
$2 wager and $2 winnings). If the total of the two dice is 8, 9, 10, 11,
or 12 then the person gets nothing (loses $2). If the total of the two
dice is 7, the person gets $0.75 back (loses $0.25). What is the
expected value of playing the game once?.
Answer: $-0.04
◉ Provide an appropriate response.
,The produce manager at a farmer's market was interested in
determining how many oranges a person buys when they buy
oranges. He asked the cashiers over a weekend to count how many
oranges a person bought when they bought oranges and record this
number for analysis at a later time. The data is given below in the
table. The random variable x represents the number of oranges
purchased and P(x) represents the probability that a customer will
buy x apples. Determine the mean number of oranges purchased by
a customer..
Answer: 3.97
◉ Provide an appropriate response.
The sum of the probabilities of a discrete probability distribution
must be.
Answer: equal to one
◉ A lab orders a shipment of 100 rats a week, 52 weeks a year, from
a rat supplier for experiments that the lab conducts. Prices for each
weekly shipment of rats follow the distribution below:
How much should the lab budget for next year's rat orders assuming
this distribution does not change. (Hint: find the expected price.).
Answer: $637.00
, ◉ Consider the discrete probability distribution to the right when
answering the following question. Find the probability that x
exceeds 4..
Answer: 0.48
◉ Consider the discrete probability distribution to the right when
answering the following question. Find the probability that x equals
4..
Answer: 0.27
◉ A random variable is.
Answer: a numerical measure of the outcome of a probability
experiment.
◉ Assume that the random variable X is normally distributed, with
mean and standard deviation Compute the probability P(57 < X <
105)..
Answer: 0.8914
◉ The amount of corn chips dispensed into a 32-ounce bag by the
dispensing machine has been identified as possessing a normal
distribution with a mean of 32.5 ounces and a standard deviation of
0.2 ounce. What chip amount represents the 67th percentile for the
bag weight distribution? Round to the nearest hundredth..
Answer: 32.59
