sample standard deviation
Give this one a try later!
s
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 60 lengths of wire, the sample mean top enclose Y would be less than 118
cm. Report your answer to four decimal places.
z=x-u/o/sqrt(N)
sampling dist
,Give this one a try later!
.9319
A poll is to be conducted a few weeks before a state election to determine which of
two candidates running for governor has greater support. The polling organization
will randomly select 500 registered voters in the state to poll. It will record each
person's response in a variable called "Preference," with possible values of {Candidate
A, Candidate B, Other}. What is the population of interest?
RESPONSE:
The purpose of the poll is to gain knowledge about how the entire electorate (i.e., the
registered voters) in the state will vote in the election. Thus, the population is all
registered voters. Although the governor of a state represents all the citizens of the
state, the population that determines the election is a subset of all citizens, namely,
the set of all registered voters. We could be more precise, though. Not all registered
voters vote, so the real population is all registered voters who actually vote.
Give this one a try later!
All registered voters in the state
not the 500 registered voters
Umbrella Corporation purchases a raw material in 55-gallon drums from a supplier.
Records for the supplier indicate that the impurity level in the material per drum has a
normal distribution with a mean of 3% and a standard deviation of 0.3%. Quality
control standards require that Umbrella return a drum to the supplier if the level of
impurity is 3.5% or more. What is the probability that Umbrella will not have to return
the drum?
Give this one a try later!
, 0.9525
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
Give this one a try later!
not -1.28
Find P(Z > -2.27) if Z is a standard normal random variable.
P(Z > -2.27)
P(Z>.0116)
1-.0116
Give this one a try later!
0.9884
A financial advisor knows that the annual returns for a particular investment follow a
normal distribution with mean 0.064 and standard deviation 0.055. 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?
68% = (u-o,u+o)
95% = (u-2o,u+2o)
99,7% = (u-3o,u+3o)
Give this one a try later!
s
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 60 lengths of wire, the sample mean top enclose Y would be less than 118
cm. Report your answer to four decimal places.
z=x-u/o/sqrt(N)
sampling dist
,Give this one a try later!
.9319
A poll is to be conducted a few weeks before a state election to determine which of
two candidates running for governor has greater support. The polling organization
will randomly select 500 registered voters in the state to poll. It will record each
person's response in a variable called "Preference," with possible values of {Candidate
A, Candidate B, Other}. What is the population of interest?
RESPONSE:
The purpose of the poll is to gain knowledge about how the entire electorate (i.e., the
registered voters) in the state will vote in the election. Thus, the population is all
registered voters. Although the governor of a state represents all the citizens of the
state, the population that determines the election is a subset of all citizens, namely,
the set of all registered voters. We could be more precise, though. Not all registered
voters vote, so the real population is all registered voters who actually vote.
Give this one a try later!
All registered voters in the state
not the 500 registered voters
Umbrella Corporation purchases a raw material in 55-gallon drums from a supplier.
Records for the supplier indicate that the impurity level in the material per drum has a
normal distribution with a mean of 3% and a standard deviation of 0.3%. Quality
control standards require that Umbrella return a drum to the supplier if the level of
impurity is 3.5% or more. What is the probability that Umbrella will not have to return
the drum?
Give this one a try later!
, 0.9525
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
Give this one a try later!
not -1.28
Find P(Z > -2.27) if Z is a standard normal random variable.
P(Z > -2.27)
P(Z>.0116)
1-.0116
Give this one a try later!
0.9884
A financial advisor knows that the annual returns for a particular investment follow a
normal distribution with mean 0.064 and standard deviation 0.055. 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?
68% = (u-o,u+o)
95% = (u-2o,u+2o)
99,7% = (u-3o,u+3o)
