Answer:
a-The average weekly profit is $1767.31
b- The probability of having a weekly profit of more than 2000 is 0.1587 or 15.87%.
Explanation:
a
The weekly average profit for the simulation is given where first the values are simulated using R which is given as below:
x<-round(rnorm(n,m,s))
Here
The values of x are as follows
[1] 36 49 30 29 34 36 32 28 32 29 32 27 40 32 30 37 43 30 42 30 31 34 36 38 28 29 32 42 36 35
[31] 37 41 34 39 37 46 34 44 45 41 41 29 36 38 35 32 36 39 30 38 40 27
Now using these values, the average of the simulation values is cacluated as follows:
mean(x)
35.3462
Now using this with the value of profit of $50 gives:
Average Profit=$50 x 35.3462
Average Profit=$1767.31
The average weekly profit is $1767.31
b-
First number of cases are required so that the value will be greater than 2000 it is given as
Number of cases=2000/50=40
So firstly the Z-score is calculated which is as below:
[tex]Z=\dfrac{x-\mu}{\sigma}\\Z=\dfrac{40-35}{5}\\Z=1[/tex]
Now the probability is given as
[tex]P(X\geq 40)=P(Z\geq 1)\\P(X\geq 40)=1-P(Z< 1)[/tex]
The value of P(Z<1) is calculated from the table which is given as
0.84134
So the equation becomes
[tex]P(X\geq 40)=1-P(Z< 1)\\P(X\geq 40)=1-0.8413\\P(X\geq 40)=0.1587[/tex]
So the probability of having a weekly profit of more than 2000 is 0.1587 or 15.87%.
