contestada

A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $2.00 per day to maintain the machine and rent the space for it. What is the mean for Y

Respuesta :

raphealnwobi

Answer:

The answer is below

Step-by-step explanation:

Let Y represent the profit per day, and x represent the number of bar sold per day. Hence:

Y = 0.25x - 2

a) The mean is given as:

[tex]\mu_y=E(Y)=E(0.25X-2) = 0.25E(X)-2\\\\But\ E(X)=mean\ of\ machine=125. Hence:\\\\E(Y)=0.25(125)-2=29.25\\\\E(Y)=\$29.25[/tex]

b) The standard deviation of y is:

[tex]\sigma_y=var(0.25X-2)\\\\\sigma_y=0.25\sigma(X)\\\\but\ \sigma_X=7,hence:\\\\\sigma_y=0.25(7)=1.75\\\\\sigma_y=\$1.75[/tex]

The mean for Y is $29.25 and this can be determined by using the given data and also by using the formula of mean.

Given :

  • A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with a mean of 125 and a standard deviation of 7.
  • His profit on each bar sold is $0.25, and it costs him $2.00 per day to maintain the machine and rent the space for it.

The equation that represents the mean for Y is:

Y = 0.25x - 2

where x is the number of bars sold in a day.

Now, the mean is evaluated as given below:

[tex]\rm \mu_y = E(Y) = E(0.25X-2)=0.25E(Y)-2[/tex]

where E(X) = 125

[tex]\rm \mu_y = 0.25(125)-2=29.25[/tex]

E(Y) = $29.25

Now, the standard deviation is given by the formula:

[tex]\sigma_y=0.25\sigma_x[/tex]

where [tex]\sigma _x = 7[/tex].

[tex]\sigma_y=0.25\times 7[/tex]

[tex]\sigma_y=1.75[/tex]

For more information, refer to the link given below:

https://brainly.com/question/23091366

Otras preguntas