Answer:
Standard deviation of the weight over a day is 1.15
Step-by-step explanation:
Since it is given that water weight is uniformly distributed between -2 to 2.
So applying formula for variance of uniformly distribution as follows,
[tex]variance=\dfrac{\left (b-a\right )^{2}}{12}[/tex]
From the given data, values of a and b is , [tex] a=-2[/tex], [tex] b=2[/tex]..
Substituting the values,
[tex]variance=\dfrac{\left (2-\left (-2 \right )\right )^{2}}{12}[/tex]
Now, [tex]-\left ( -2 \right )=2[/tex]
[tex]variance=\dfrac{\left (2+2\right )^{2}}{12}[/tex]
[tex]variance=\dfrac{\left (4\right )^{2}}{12}[/tex]
[tex]variance=\dfrac{16}{12}[/tex]
Dividing the fraction by 4,
[tex]variance=\dfrac{4}{3}[/tex]
So, the value of variance is [tex]\dfrac{4}{3}[/tex]
The formula for standard deviation is given as,
[tex]Standard\:deviation=\sqrt{variance}[/tex]
Substituting the value,
[tex]Standard\:deviation=\sqrt{\dfrac{4}{3}}[/tex]
[tex]Standard\:deviation=1.15470[/tex]
Rounding to 2 decimal places,
[tex]Standard\:deviation=1.15[/tex]
So, the value of standard deviation is 1.15.
