Answer:
Standard Deviation = 3.22
Variance = 10.36
Step-by-step explanation:
x P(x) x × P(x) x² x² × P(x)
19 0.20 3.8 361 72.2
10 0.20 2 100 20
11 0.30 3.3 121 36.3
12 0.20 2.4 144 28.8
13 0.10 1.3 169 16.9
____________________________________________
12.8 174.2 => Total
Mean Formula
[tex]\mu_x = \sum(x \times P(x))[/tex] [tex]= 12.8[/tex]
[tex]\mu_x^2 = 163.84[/tex]
Variance Formula
[tex]\sigma _x^2 = \sum[x^2 \times P(x)] - \mu_x^2[/tex]
[tex]= 174.2- 163.84\\\\=10.36[/tex]
Standard Deviation Formula
[tex]Standard\ deviation, \ \sigma_x = \sqrt{Variance}[/tex]
[tex]=\sqrt{10.36}\\\\=3.218[/tex]
