BANA 2372 TEST QUESTONS
WITH CORRECT ANSWERS
In the U.S., it has been claimed that adults between the ages of 18 and 30 send an
average of 45.4 text messages per day, with a standard deviation of 24.5. If a random
sample of 104 adults in this age group were collected, what would be the mean of the
sampling distribution of the sample mean, to one decimal place? Hint: This is primarily a
question about one of the properties of the sampling distribution of the sample mean.
Reread the theorems ("math facts") given in the PowerPoint slide and/or the Course
Packet. - Answer-
In the U.S., it has been claimed that adults between the ages of 18 and 30 send an
average of 52.8 text messages per day, with a standard deviation of 24.2. If a random
sample of 109 adults in this age group were collected, what would be the standard
deviation of the sampling distribution of the sample mean, to one decimal place?
Hint 1: This is primarily a question about one of the properties of the sampling
distribution of the sample mean. Reread the theorems ("math facts") given in the
PowerPoint slides and/or the Course Packet.
Hint 2: Although the setup of this problem is similar to another problem in this
assignment, the specific numbers will differ. - Answer-
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
A machine in a manufacturing process that produces lengths of wire is "calibrated" (i.e.,
operating properly) if the average length of the wire is 117 cm. Natural variability in the
process results in some wires being slightly longer or shorter than this, so the length of
wire this machine produces is actually a random variable. It is known that the process
has a standard deviation of 5.2 cm. Find the probability that, in a random sample of 36
lengths of wire, the sample mean would be less than 118 cm. Report your answer to
four decimal places. - Answer-.8749
An analyst working for a social media company has determined that the mean number
of "friends" that users of the company's main service (a smartphone app) have is 190,
with a standard deviation of 250. What is the probability that, in any random sample of
70 users, the mean number of friends those users have, , would be less than 150?
Report your answer to four decimal places. - Answer-
WITH CORRECT ANSWERS
In the U.S., it has been claimed that adults between the ages of 18 and 30 send an
average of 45.4 text messages per day, with a standard deviation of 24.5. If a random
sample of 104 adults in this age group were collected, what would be the mean of the
sampling distribution of the sample mean, to one decimal place? Hint: This is primarily a
question about one of the properties of the sampling distribution of the sample mean.
Reread the theorems ("math facts") given in the PowerPoint slide and/or the Course
Packet. - Answer-
In the U.S., it has been claimed that adults between the ages of 18 and 30 send an
average of 52.8 text messages per day, with a standard deviation of 24.2. If a random
sample of 109 adults in this age group were collected, what would be the standard
deviation of the sampling distribution of the sample mean, to one decimal place?
Hint 1: This is primarily a question about one of the properties of the sampling
distribution of the sample mean. Reread the theorems ("math facts") given in the
PowerPoint slides and/or the Course Packet.
Hint 2: Although the setup of this problem is similar to another problem in this
assignment, the specific numbers will differ. - Answer-
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
A machine in a manufacturing process that produces lengths of wire is "calibrated" (i.e.,
operating properly) if the average length of the wire is 117 cm. Natural variability in the
process results in some wires being slightly longer or shorter than this, so the length of
wire this machine produces is actually a random variable. It is known that the process
has a standard deviation of 5.2 cm. Find the probability that, in a random sample of 36
lengths of wire, the sample mean would be less than 118 cm. Report your answer to
four decimal places. - Answer-.8749
An analyst working for a social media company has determined that the mean number
of "friends" that users of the company's main service (a smartphone app) have is 190,
with a standard deviation of 250. What is the probability that, in any random sample of
70 users, the mean number of friends those users have, , would be less than 150?
Report your answer to four decimal places. - Answer-
