Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day. x 25 50 75 100 Total P(x) .24 .38 .30 .08 1.00 (a) Calculate the expected value and standard deviation of this random variable X. (Round your answers to 2 decimal places.)

Sagot :

MrRoyal

Probabilities are used to determine the chances of an event.

  • The expected value is: 55.5
  • The standard deviation is 22.52

(a) The expected value

This is the mean of the distribution, and it is calculated using:

[tex]\mathbf{E(x) = \sum x \cdot P(x)}[/tex]

So, we have:

[tex]\mathbf{E(x) = 25 \times 0.24 + 50 \times 0.38 + 75 \times 0.30 + 100 \times 0.08 }[/tex]

Using a calculator, we have:

[tex]\mathbf{E(x) = 55.5}[/tex]

Hence, the expected value is: 55.5

(b) The standard deviation

This is calculated using:

[tex]\mathbf{\sigma = \sqrt{E(x^2) - (E(x))^2}}[/tex]

Where:

[tex]\mathbf{E(x^2) = \sum x^2 \cdot P(x)}[/tex]

So, we have:

[tex]\mathbf{E(x^2) = 25^2 \times 0.24 + 50^2 \times 0.38 + 75^2 \times 0.30 + 100^2 \times 0.08 }[/tex]

[tex]\mathbf{E(x^2) = 3587.5 }[/tex]

So, we have:

[tex]\mathbf{\sigma = \sqrt{E(x^2) - (E(x))^2}}[/tex]

[tex]\mathbf{\sigma = \sqrt{3587.5 - 55.5^2}}[/tex]

[tex]\mathbf{\sigma = \sqrt{3587.5 - 3080.25}}[/tex]

[tex]\mathbf{\sigma = \sqrt{507.25}}[/tex]

[tex]\mathbf{\sigma = 22.52}[/tex]

Hence, the standard deviation is 22.52

Read more about expected values and standard deviations at:

https://brainly.com/question/17088771

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.