BANA 2372 HOLLANDER FINAL EXAM
COMPREHENSIVE SCRIPT 2026 FULL STUDY
GUIDE COMPLETE RESPONSES
◉ Because of slight, natural variation in the manufacturing
equipment, the amount of caffeine in Umbrella Corporation's new
energy drink, called "OMZ," is actually a normal random variable
with a mean of 80mg and a standard deviation of 0.083 mg. What is
the probability that a randomly selected can has more than 80.08 mg
of caffeine? Enter the closest answer. Enter your answer as a
decimal, not a percent. For example, if the answer is 0.3161, enter
0.3161, NOT 31.61%. Answer: .1685
◉ Because of slight, natural variation in the manufacturing
equipment, the amount of caffeine in Umbrella Corporation's new
energy drink is actually a normal random variable with a mean of
80mg and a standard deviation of 0.083 mg. What is the probability
that a randomly selected can has less than 80.03 mg of caffeine?
Enter the closest answer. Enter your answer as a decimal, not a
percent. For example, if the answer is 0.3161, enter 0.3161, NOT
31.61%. Answer: not .36145
◉ Because of slight, natural variation in the manufacturing
equipment, the amount of caffeine, Y, in Umbrella Corporation's new
energy drink called "OMZ" is actually a normally distributed random
variable with a mean of 80mg and a standard deviation of 0.083 mg.
,What is the probability that a randomly selected can has more than
80.04 mg of caffeine? Enter your answer as a decimal, not a percent.
For example, if the answer is 0.3161, enter 0.3161, NOT 31.61%.
Answer: .3149
◉ The heights of U. S. women are normally distributed with a mean
of 63.6 inches and a standard deviation of 2.6 inches. What is the
probability of a randomly selected woman having a height smaller
than 70 inches? Enter your answer as a decimal, not a percent. For
example, if the answer is 0.3161, enter 0.3161, NOT 31.61%.
Answer: .9931
◉ A financial advisor knows that the annual returns for a particular
investment follow a normal distribution with mean 0.061 and
standard deviation 0.051. Using the 68-95-99.7 rule, what would be
the most that a client who is interested in the investment could
reasonably expect to lose, to three decimal places? Answer: not .156
◉ Suppose Z is a standard normal random variable. What is P(Z > -
0.83), to three decimal places? Answer: .7967
◉ If Z is a standard normal random variable, find P(-1.96 < Z < 1.96)
Answer: 0.95
◉ If Z is a standard normal random variable, find z0.003 Answer:
not -2.75
, ◉ If Z is a standard normal random variable, find find z0.0643.
Answer: not -1.52
◉ Find the value mc018-1.jpg on the standard normal distribution.
Choose the closest answer. Answer: 2.33
◉ Suppose Z is a standard normal random variable. Find the value of
z subscript bevelled alpha over 2 end subscript such that P left
parenthesis minus z subscript bevelled alpha over 2 end subscript
less or equal than Z less or equal than z subscript bevelled alpha
over 2 end subscript right parenthesis equals 0.80 Answer: not -1.28
◉ Suppose you imagine repeatedly taking random samples of size
100 from a population with a mean μ = 50 and a standard deviation
σ = 20. Then the __________ says that the ___________ has approximately
a _________ distribution with a mean equal to _________ and a standard
deviation equal to __________. Answer: central limit theorem
sampling distribution of the sample mean
normal
50
2
◉ An analyst working for a social media company has determined
that the mean number of "friends" that users of the company's main
COMPREHENSIVE SCRIPT 2026 FULL STUDY
GUIDE COMPLETE RESPONSES
◉ Because of slight, natural variation in the manufacturing
equipment, the amount of caffeine in Umbrella Corporation's new
energy drink, called "OMZ," is actually a normal random variable
with a mean of 80mg and a standard deviation of 0.083 mg. What is
the probability that a randomly selected can has more than 80.08 mg
of caffeine? Enter the closest answer. Enter your answer as a
decimal, not a percent. For example, if the answer is 0.3161, enter
0.3161, NOT 31.61%. Answer: .1685
◉ Because of slight, natural variation in the manufacturing
equipment, the amount of caffeine in Umbrella Corporation's new
energy drink is actually a normal random variable with a mean of
80mg and a standard deviation of 0.083 mg. What is the probability
that a randomly selected can has less than 80.03 mg of caffeine?
Enter the closest answer. Enter your answer as a decimal, not a
percent. For example, if the answer is 0.3161, enter 0.3161, NOT
31.61%. Answer: not .36145
◉ Because of slight, natural variation in the manufacturing
equipment, the amount of caffeine, Y, in Umbrella Corporation's new
energy drink called "OMZ" is actually a normally distributed random
variable with a mean of 80mg and a standard deviation of 0.083 mg.
,What is the probability that a randomly selected can has more than
80.04 mg of caffeine? Enter your answer as a decimal, not a percent.
For example, if the answer is 0.3161, enter 0.3161, NOT 31.61%.
Answer: .3149
◉ The heights of U. S. women are normally distributed with a mean
of 63.6 inches and a standard deviation of 2.6 inches. What is the
probability of a randomly selected woman having a height smaller
than 70 inches? Enter your answer as a decimal, not a percent. For
example, if the answer is 0.3161, enter 0.3161, NOT 31.61%.
Answer: .9931
◉ A financial advisor knows that the annual returns for a particular
investment follow a normal distribution with mean 0.061 and
standard deviation 0.051. Using the 68-95-99.7 rule, what would be
the most that a client who is interested in the investment could
reasonably expect to lose, to three decimal places? Answer: not .156
◉ Suppose Z is a standard normal random variable. What is P(Z > -
0.83), to three decimal places? Answer: .7967
◉ If Z is a standard normal random variable, find P(-1.96 < Z < 1.96)
Answer: 0.95
◉ If Z is a standard normal random variable, find z0.003 Answer:
not -2.75
, ◉ If Z is a standard normal random variable, find find z0.0643.
Answer: not -1.52
◉ Find the value mc018-1.jpg on the standard normal distribution.
Choose the closest answer. Answer: 2.33
◉ Suppose Z is a standard normal random variable. Find the value of
z subscript bevelled alpha over 2 end subscript such that P left
parenthesis minus z subscript bevelled alpha over 2 end subscript
less or equal than Z less or equal than z subscript bevelled alpha
over 2 end subscript right parenthesis equals 0.80 Answer: not -1.28
◉ Suppose you imagine repeatedly taking random samples of size
100 from a population with a mean μ = 50 and a standard deviation
σ = 20. Then the __________ says that the ___________ has approximately
a _________ distribution with a mean equal to _________ and a standard
deviation equal to __________. Answer: central limit theorem
sampling distribution of the sample mean
normal
50
2
◉ An analyst working for a social media company has determined
that the mean number of "friends" that users of the company's main
