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Answer:
The amount $15000 is divided as
in 2% = $7000
in 5% = $8000
Step-by-step explanation:
It is given that the total amount is $15000 and rates of interests are 2% and 5%.
<em>Let the amount invested in 2% be "x", so the amount invested in 5% is (15000 - x).</em>
The annual interest on x part is given as,
=
Similarly, The annual interest on (15000 - x) part is given as,
=
the total annual interest is given as $540
Thus, <em>540 = </em>
<em>54000 = </em>
<em>21000 = 3(x)</em>
x = = 7000
Thus the shares are $7000 and (15000 - 7000) $8000 .
Answer:
a) Figure attached
b)
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 95%
c)
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 34+34+13.5+2.35%=83.85%
d)
And using the z score we got:
And that correspond to approximately 0.15%
Step-by-step explanation:
Part a
For this case we can see the figure attached.
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 b
Let X the random variable that represent the length of human pregnancy of a population, and for this case we know that:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 95%
Part c
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 34+34+13.5+2.35%=83.85%
Part d
We want this probability:
And using the z score we got:
And that correspond to approximately 0.15%
