A statistics student is trying to decide whether she should take a gamble and play
Bingo. The average Bingo player earns $9 per game, distributed normally, with a
population standard deviation of $8 . If a sample of 25
...
A statistics student is trying to decide whether she should take a gamble and play
Bingo. The average Bingo player earns $9 per game, distributed normally, with a
population standard deviation of $8 . If a sample of 25 Bingo players are selected
at random from the population, select the expected mean of the sampling
distribution and the standard deviation of the sampling distribution below.
Well done! You got it right.
σx¯=$0.32
σx¯=$8
σx¯=$1.60
μx¯=$9
μx¯=$1.80
μx¯=$0.36
Answer Explanation
Correct answer:
σx¯=$1.60
μx¯=$9
The standard deviation of the sampling distribution is:
σx¯=σn−−√=$825−−√=$1.60
When the distribution is normal the mean of the sampling distribution is equal to
the mean of the population μx¯=μ
Question
A well known social media company is looking to expand their online presence by
creating another platform. They know that they current average 2,500,000
users each day, with a standard deviation of 625,000 users. If they randomly
sample 50 days to analyze the use of their existing technology, identify each of the
following, rounding to the nearest whole number if necessary:
Answer 1:
Not quite - review the answer explanation to help get the next one.
mu is equal to$\mu=$μ= 2 comma 500 comma 000$$2,500,0002 comma 500 comma 000 -
correct users
sigma is equal to$\sigma=$σ= 625 comma 000$$625,000625 comma 000 - correct users
n is equal to$n=$n= 50$$5050 - correct
mu sub line segment x is equal to $\mu_{\overline{x}}=$μghx= 625 comma 00050$
$625,00050625 comma 00050 - incorrect users
sigma sub line segment x is equal to$\sigma_{\overline{x}}=$σghx= 88 comma 388$$88,38888
comma 388 - correct users
response - incorrect
Correct answers:
Answer 2:
That's not right - let's review the answer.
mu is equal to$\mu=$μ= 2 comma 500 comma 000$$2,500,0002 comma 500 comma 000 -
correct users
sigma is equal to$\sigma=$σ= 625 comma 000$$625,000625 comma 000 - correct users
n is equal to$n=$n= 50$$5050 - correct
mu sub line segment x is equal to $\mu_{\overline{x}}=$μghx= 625 comma 00050$
$625,00050625 comma 00050 - incorrect users
sigma sub line segment x is equal to$\sigma_{\overline{x}}=$σghx= 88 comma 388$$88,38888
comma 388 - correct users
response - incorrect
Correct answers:
Answer Explanation
mu is equal to$\mu=$μ= 1$$1 - no response given users
sigma is equal to$\sigma=$σ= 2$$2 - no response given users
n is equal to$n=$n= 3$$3 - no response given
mu sub line segment x is equal to $\mu_{\overline{x}}=$μghx= 4$$4 - no response given users
sigma sub line segment x is equal to$\sigma_{\overline{x}}=$σghx= 5$$5 - no response
given users
Correct answers:
12500000$2500000$2500000
2625000$625000$625000
350$50$50
42500000$2500000$2500000
588388$88388$88388
We are given population mean μ=2,500,000 and population standard
deviation σ=625,000 , and want to find the mean and standard error of the
sampling distribution, μx¯ and σx¯ for samples of size n=50 .
By the Central Limit Theorem, the means of the two distributions are the same:
μx¯=μ=2,500,000
To find the Standard Deviation of the sampling distribution, we divide the
population standard deviation by the square root of the sample size:
σx¯=σn−−√=625,00050−−√≈88,388
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Understand sampling distributions and the Central Limit Theorem for Means
Question
A family of statisticians is trying to decide if they can afford for their child to play
youth baseball. The cost of joining a team is normally distributed with a mean of
$750 and a standard deviation of $185 . If a sample of 40 teams is selected at
random from the population, select the expected mean and standard deviation of
the sampling distribution below.
Correct! You nailed it.
σx¯=$185
σx¯=$29.25
σx¯=$4.63
μx¯=$118.59
μx¯=$18.75
μx¯=$750
Answer Explanation
Correct answer:
σx¯=$29.25
μx¯=$750
The standard deviation of the sampling distribution
σx¯=σn−−√=$18540−−√=$29.25
When the distribution is normal the mean of the sampling distribution is equal to
the mean of the population μx¯=μ=$750 .
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There is an error in the instruction or question.
This looks broken...
A graph/image/equation/video isn't working
I cannot enter my answer.
A problem is preventing me from entering an answer to this question.
I have an idea!
I have some feedback/suggestions.
Question
A bank is reviewing its risk management policies with regards to mortgages. To
minimize the risk of lending, the bank wants to compare the typical mortgage owed
by their clients against other homebuyers. The average mortgage owed by
Americans is $306,500 , with a standard deviation of $24,500 . Suppose a
random sample of 150 Americans is selected.
Identify each of the following, rounding your answers to the nearest cent when
appropriate:
Answer 1:
Keep trying - mistakes can help
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