High School

We appreciate your visit to In a box are four cards numbered 5 10 15 and 20 Two cards are taken out at random without replacement and x is the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

In a box are four cards numbered 5, 10, 15, and 20. Two cards are taken out at random without replacement, and \( x \) is the total of the numbers on the two cards.

Answer :

By using the formula for mean and variance, it can be calculated that

Mean of X = 25

Variance of X = 51.67

What is mean and variance?

Suppose there is a data set. Mean gives the average of the values of the data set

Variance is the square of the sum of deviation from mean.

Let x be the total; of the numbers on the two card

Possible values of X= 15, 20, 25, 30, 35

P(X = 15) = [tex]\frac{2}{12}[/tex]

P(X = 20) = [tex]\frac{2}{12}[/tex]

P(X = 25) = [tex]\frac{4}{12}[/tex]

P(X= 30) = [tex]\frac{2}{12}[/tex]

P(X = 35) = [tex]\frac{2}{12}[/tex]

Mean of X =

[tex]15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25[/tex]

Variance of X =

= [tex](225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67[/tex]

To learn more about mean and variance, refer to the link-

https://brainly.com/question/25639778

#SPJ4

Complete Question

In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .

Thanks for taking the time to read In a box are four cards numbered 5 10 15 and 20 Two cards are taken out at random without replacement and x is the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Other Questions