Answer:
The standard deviation of x is 2.8867
Step-by-step explanation:
The standard deviation of variable x that follows a uniform distribution is calculated as:
[tex]s = \sqrt{\frac{(b-a)^{2} }{12} }[/tex]
Where (a,b) is the interval where x is defined.
So, replacing a by -4 and b by 6, the standard deviation is:
[tex]s = \sqrt{\frac{(6-(-4))^{2} }{12} }[/tex]
[tex]s = \sqrt{\frac{(10)^{2} }{12} }[/tex]
[tex]s=\sqrt{\frac{100}{12} }[/tex]
[tex]s=\sqrt{8.3333}[/tex]
[tex]s=2.8867[/tex]
