Sarah has a pond in the shape of a half sphere in her back yard. The pond currently holds 1,071.79 cubic inches of water. What is the radius of the pond?

1071,79 = (1/2) × (4/3) πr³

1071,79 = (2/3) × 3,14 × r³

1071,79 = 2,093333 × r³

512 = r³

8³ = r³

8 = r

The given data for this problem are as follows:
x         0           1           2           3         4 
p(x)   0.49     0.05     0.32     0.07     0.07

we are asked to get the mean of the random variable x

to get the mean, we use the formula
x̄  = σxp(x)
x̄ = 0(0.49) + 1(0.05) + 2(0.32) + 3(0.07) + 4(0.07) = 4.97

to get the standard deviation, we use the formula
σ =√[ ∑x²p(x) -   x̄ ]²
substituting
σ =  √[ (0²(0.49) + 1²(0.05) + 2²(0.32) + 3²(0.07) + 4²(0.07)) - 4.97]²
σ = 1.89

so, the mean is 4.97 and the standard deviation is 1.89