The time it takes a printer to print a job is an Exponential random variable with the expectation of 12 seconds. You send a job
1 answer:
Answer:
0.8753
Step-by-step explanation:
Calculate the probability that your job will be ready before 10.01 am
Here, the parameter of an Exponential is E(X)=12
Now, to calculate the third job probability, it follows Poisson Distribution with parameter 1/λ
Therefore, E(Y) =1/12
Here, The third job will be ready for 10:01 AM, then E(Y)=61/12
Therefore, the required probability is
=1- POISSON(3,5,true)
=1-0.1246
=0.8753
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Answer:
Part 1)
See Below.
Part 2)
Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:
We want to verify that the expression:
Is the linear approximation for the function:
At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:
Simplify. Hence:
Then the slope of the linear approximation at <em>x</em> = 0 will be:
And the value of the function at <em>x</em> = 0 is:
Thus, the linear approximation will be:
Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:
By definition:
Therefore:
We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:
