8 total pens....4 are black
first pick, probability of being black is 4/8
2nd pick. without replacing, probability is 3/7
probability of a black pen picked first and then another black pen picked again is : 4/8 * 3/7 = 12/56 = 0.21
I would add 7 to get ...
... 2x² = 16
then divide by 2 to get
... x² = 8
Now, I would take the square root, recognizing that both positive and negative values will solve the problem.
... x = ±√8
The root can be simplified, so we have ...
... x = ±2√2
_____
The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.
... 2x² -16 = 0 . . . . subtract 9
... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula
... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result
Answer:
a

b
Step-by-step explanation:
From the question we are told that
The daily demand is 
The standard deviation is 
The service probability is 
The number of chips in the inventory is 
The number of days in his monthly is 
The lead time is 
Generally the number he should order (optimal order ) is mathematically represented as

Here
is the monthly standard deviation which is mathematically evaluated as

=> 
=> 
Also z-value for the 95% service probability from the z-table is 1.96
So

=> 
For the maximum order quantity k = 0
So

=>
=>
Answer:
Mean = 3.4
Variance = 1.088
Standard deviation = 1.0431
Step-by-step explanation:

The mean of a binomial distribution with parameters N (the number of trials) and p (the probability of success for each trial) is 
Thus,

The variance of the binomial distribution is
, where
is the variance of the binomial distribution, so

The standard deviation
is the square root of the variance
so
