The standard deviation of the pack of gaming cards is 4
The entry on the table is given as:
x | $10 | $20
P(x) | 20% | 80%
Also, we have:
[tex]\mu_x = 18[/tex]
The standard deviation of a dataset is calculated using:
[tex]\sigma_x = \sqrt{E(x^2) - \mu_x^2}[/tex]
Where:
[tex]E(x^2) = \sum x^2 \times P(x)[/tex]
This gives
[tex]E(x^2) = 10^2 \times 20\% + 20^2 \times 80\%[/tex]
[tex]E(x^2) = 340[/tex]
[tex]\sigma_x = \sqrt{E(x^2) - \mu_x^2}[/tex] becomes
[tex]\sigma_x = \sqrt{340 - 18^2}[/tex]
[tex]\sigma_x = \sqrt{340 - 324}[/tex]
[tex]\sigma_x = \sqrt{16}[/tex]
Take positive square root
[tex]\sigma_x = 4[/tex]
Hence, the standard deviation of the dataset is 4
Read more about standard deviations at:
https://brainly.com/question/475676
