if $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in
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Answer:
0.6826 = 68.26% probability that you have values in this interval.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
X~N(8, 1.5)
This means that
What is the probability that you have values between (6.5, 9.5)?
This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So
X = 9.5
has a p-value of 0.8413.
X = 6.5
has a p-value of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability that you have values in this interval.
Assuming ya meant 
to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos
for the pythaogreaon identity
divide both sides by
since 
subsitute
recall that
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore
so we get
decompose them into
and 
to get 
multiply by
to get
we can furthur simlify to get
the expression simplifies to tan(x)sin(x)
to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos
for the pythaogreaon identity
divide both sides by
subsitute
recall that
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore
so we get
decompose them into
multiply by
we can furthur simlify to get
the expression simplifies to tan(x)sin(x)