Amachine that fills bottles with a beverage has a fill volume whose mean is 25.01 ounces, with a standard deviation of 0.02 ounces. a case consists of 24 bottles randomly sampled from the output of the machine. find the standard deviation of the total volume of the beverage in the case.

The standard deviation in the case is 0.004.

The population mean is 25.01 and the population standard deviation is 0.002.  To find the sample standard deviation, we use 
σₓ = σ/(√n), where σ is the population standard deviation and n is the sample size.  Using our information we have:
σₓ = 0.02/(√24) = .004.

We are given the height of Joe which is 1.6 meters, the length of his shadow is 2 meters when he stands 3 meters from the base of the floodlight. 

First, we have to illustrate the problem. Then we can observe two right triangles formed, one is using Joe and the length of the shadow, the other is the floodlight and the sum of the distance from the base plus the length of the shadow. To determine the height of the floodlight, use ratio and proportion:

1.6 / 2 = x / (2 +3)

where x is the height of the flood light

solve for x, x = 4. Therefore, the height of the floodlight is 4 meters.