A dollar bill is about 0.00011 meter thick. What is this thickness is scientific notation?
1 answer:
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Answer:
a)
b)
c)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the number of people of a population, and for this case we know that:
Where and
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean is given by:
And we want to find this probability:
And using a calculator, excel or the normal standard table we have that:
Part b
And using a calculator, excel or the normal standard table we have that:
Part c
For this case we want this probability:
And using a calculator, excel or the normal standard table we have that:
Answer
,
,
Step-by-step explanation:
Given that
For the term .
Limits for is from
to
and for
is from
to
and the region
, for this double integration is the shaded region as shown in graph 1.
Now, reverse the order of integration, first integrate with respect to then with respect to
. So, the limits of
become from
to
and limits of
become from
to
as shown in graph 2.
So, on reversing the order of integration, this double integration can be written as
Similarly, for the other term .
Limits for is from
to
and limits for
is from
to
and the region
, for this double integration is the shaded region as shown in graph 3.
Now, reverse the order of integration, first integrate with respect to then with respect to
. So, the limits of
become from
to
and limits of
become from
to
as shown in graph 4.
So, on reversing the order of integration, this double integration can be written as
Hence, from equations ,
and
, on reversing the order of integration, the required expression is
Now, compare the RHS of the equation with
We have,
and
.
