In a recent study reported Oct.29, 2012 on the Flurry Blog, the mean age of tablet users is 35 years. Suppose the standard deviation is ten years. The sample size is 39.
What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution?
Find the probability that the sum of the ages is between 1,400 and 1,500 years.
Find the 90
th percentile for the sum of the 39 ages.
μ
Σx =
nμ
x = 1,365 and
σ
Σx =
= 62.4
The distribution is normal for sums by the central limit theorem.
P (1400<
Σ
x <1500) =
normalcdf (1400,1500,(39)(35),(
)(10)) = 0.2723
Let
k = the 90
th percentile.
k =
invNorm (0.90,(39)(35),(
)
(10)) = 1445.0
The mean number of minutes for app engagement by a tablet user is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample of size 70.
What are the mean and standard deviation for the sums?
Find the 95
th percentile for the sum of the sample. Interpret this value in a complete sentence.
Find the probability that the sum of the sample is at least ten hours.
μ
Σx =
nμ
x = 70(8.2) = 574 minutes and
σ
Σx =
=
(1) = 8.37 minutes
Let
k = the 95
th percentile.
k = invNorm
(0.95,(70)(8.2),
(1)) = 587.76 minutes
Ninety five percent of the app engagement times are at most 587.76 minutes.
ten hours = 600 minutes
P (Σ
x ≥ 600) =
normalcdf (600,E99,(70)(8.2),
(1)) = 0.0009
The mean number of minutes for app engagement by a table use is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample size of 70.
What is the probability that the sum of the sample is between seven hours and ten hours? What does this mean in context of the problem?
Find the 84
th and 16
th percentiles for the sum of the sample. Interpret these values in context.
7 hours = 420 minutes
10 hours = 600 minutes
normalcdf
This means that for this sample sums there is a 99.9% chance that the sums of usage minutes will be between 420 minutes and 600 minutes.
Since 84% of the app engagement times are at most 582.32 minutes and 16% of the app engagement times are at most 565.68 minutes, we may state that 68% of the app engagement times are between 565.68 minutes and 582.32 minutes.
Farago, Peter. “The Truth About Cats and Dogs: Smartphone vs Tablet Usage Differences.” The Flurry Blog, 2013. Posted October 29, 2012. Available online at http://blog.flurry.com (accessed May 17, 2013).
Chapter review
The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution even if the original population is not normally distributed. Additionally, if the original population has a mean of
μ
X and a standard deviation of
σ
x , the mean of the sums is
nμ
x and the standard deviation is
(
σ
x ) where
n is the sample size.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
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Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
