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
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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 .
