Roderick is counting the change on his dresser. he has twice as many pennies as he does dimes. he has twice the amount of dimes
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Answer:
The standard deviation for the distribution of scores is 6.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 78
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Empirical Formula:
- Almost all the data lies within three standard deviation from mean for a normal data.
- for this rule almost all the data lies within on tandard deviation from the mean.
68% of the scores fall between 72 and 84, thus, we can write:
Thus, the standard deviation for the distribution of scores is 6.
Take partial derivatives and set them equal to 0:
We find one critical point within the boundary of the disk at
. The Hessian matrix for this function is
which is positive definite, and incidentally independent of
and 
, so 
attains a minimum 
.
Meanwhile, we can parameterize the boundary by
with 
, which gives
with critical points at
At these points, we get
so we attain a maximum only when
, which translates to 
.
We find one critical point within the boundary of the disk at
which is positive definite, and incidentally independent of
Meanwhile, we can parameterize the boundary by
with critical points at
At these points, we get
so we attain a maximum only when