Suppose that upper x has a discrete uniform distribution f left-parenthesis x right-parenthesis equals startlayout left-brace1st row 1st column 1 divided by 3, 2nd column x equals 1,2,3 2nd row 1st column 0, 2nd column otherwise endlayout a random sample of n equals 35 is selected from this population. find the probability that the sample mean is greater than 2.1 but less than 2.5. express the final answer to four decimal places (e. g. 0.9876).

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).