Answer:The mean number of checks written per day = 0.3370
The standard deviation = 0.5805
The variance = 0.3370
Step-by-step explanation:
Let the random variable x represent the number of checks he wrote in one day.
Given : The number of checks written in last year = 123
Let the number of days in the year must be 365.
Now, the mean number of checks written per day will be :-

We know that in Poisson distribution , the variance is equals to the mean value .


Thus, Standard deviation = 0.5805
Part A:
Consider from x = -5 to x = -4, they are 1 unit apart and the difference of their outputs is given by:
-3 - (-11) = -3 + 11 = 8.
Thus, the value of the output increases by 8 units for each one unit increase in the input.
Part B:
Consider from x = -3 to x = -1, they are 2 units apart and the difference of their outputs is given by:
21 - 5 = 16.
Thus, the value of the output increases by 16 units for each two units increase in the input.
Part C:
Consider from x = 0 to x = 3, they are 3 units apart and the difference of their outputs is given by:
53 - 29 = 24.
Thus, the value of the output increases by 24 units for each three units increase in the input.
Part D:
It can be noticed that the ratio difference in the outputs to the input intervals are equal for all the given input intervals.
i.e 8 / 1 = 16 / 2 = 24 / 3.
The value of the height of the cylinder is 25cm.
According to the statement
we have to find that the height pf the cylinder with the given value of the volume.
So, For this purpose we know that the
The volume of a cylinder is the density of the cylinder which finds that the amount of material it can carry. Cylinder's volume is given by the formula, πr^2h.
From the given information:
The volume of a cylinder is 225π cubic inches, and the radius of the cylinder is 3 inches.
Then
volume = πr^2h
225π = π3^2h
Now, solve it then
225 = 9h
h = 25.
The value becomes 25.
So, The value of the height of the cylinder is 25cm.
Learn more about volume of a cylinder here
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The answer is 8
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