An article suggests the uniform distribution on the interval (6.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.(a) What are the mean and variance of depth

The mean of depth is 12.75cm.

The variance of depth is of 13.02 cm².

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

The variance of the uniform distribution is given by:

Uniform distribution on the interval (6.5, 19)

This means that:

So

Mean:

The mean of depth is 12.75cm.

Variance:

The variance of depth is of 13.02 cm².

We know that formula for volume of cone is 1/3 πr² h where r is radius and h is height.

Now we know that r is 2 and volume is 29 so we can set up equation like this:

29 = 1/3 π (2)² h

Now we need to solve for h:

29 = 4/3 π h

Divide both sides by 4/3 π:

29 / (4/3 π) = h

87 / (4π) = h

Use calculator here

h ≈ 6.92675159

Round to nearest hundredth:

h ≈ 6.93

Final 6.93