Recall that for

, i.e. a random variable

following a binomial distribution over

trials and with probability parameter

,

So you have




The expected value of

is simply

, while the standard deviation is

. In this case, they are

and

, respectively.
I believe it’s x=2.5 or x=2 1/2 or x=5/2
They are all the same answers in different forms . Hope it’s right
Answer:
Proof in explanation.
Step-by-step explanation:
I'm going to attempt this by squeeze theorem.
We know that
is a variable number between -1 and 1 (inclusive).
This means that
.
for all value
. So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

By squeeze theorem, if 
and
, then we can also conclude that
.
So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at
.

.
We can finally conclude that
by squeeze theorem.
Some people call this sandwich theorem.
Sorry I don't know that question.
We know that the profit from an item is the sale price minus the cost price. Thus,
1269 - 0.2x² - 830 - 398x
P(x) = -0.2x² - 398x + 439
Local maxima are located at the points where the first derivative of a function are 0
P'(x) = -0.4x - 398
398 = -0.4x
x = -995
There is only one maximum so the average value is -995