Answer:
a)
And we can find this probability using the normal standard table or excel and we got:
b)
And we can find this probability using the complement rule and the normal standard table or excel and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel and we got:
Part b
And we can find this probability using the complement rule and the normal standard table or excel and we got:
The corresponding homogeneous ODE has characteristic equation
with roots at
, thus admitting the characteristic solution

For the particular solution, assume one of the form



Substituting into the ODE gives



Then the general solution to this ODE is



Assume a solution of the form



Substituting into the ODE gives



so the solution is



Assume a solution of the form


Substituting into the ODE gives



so the solution is

Hold on let me go do my research I’ll brb .
here is your answer hope you will understand it
Mode = is the number with the highest frequency so the answer is 4.
Mean = the average so the answer is 3+4+5+4+6+4+7=33 so 33/7=4.7 (rounded to the nearest one decimal).
Median = the middle number, so the answer is 4.