Answered

Connect with experts and get insightful answers to your questions on IDNLearn.com. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.

Weekly demand for tennis balls at The Racquet Club is normally distributed , with a mean of 35 cases and a standard deviation of 5 cases . The club gets a profit of $ 50 per case (a ) Simulate 52 weeks of demand and calculate the average weekly profit. Make all demand values integers in your model . (b ) What is the probability that weekly profit will be \$2,00 or more ?

Sagot :

Danialaminidn

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

  • round converts all the values of the simlation to integer.
  • rnorm is the command for simulation
  • n is the number of values which is 52 in this case
  • m is the mean of the values which is 35
  • s is the value of standard deviation which is 5 cases.

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%.

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.