Population of dogs mean rate 26 pounds and a deviation of 3.6 pounds, Population of cats mean rate 10.5 and a deviation of 1.9 if a dog weights 24 pounds and a cat weights 19 pounds. which weighs more for its population?
Z = (score-mean)/SD
Which has the highest value?
However, you don't need to go through this, because (assuming no typos) one value is above the mean and the other is below.
To determine which animal weighs more in relation to its population, we need to compare the weights of the individual animals in reference to their respective populations.
Let's start with the dog:
1. Calculate the Z-score for the weight of the dog:
Z-score = (Individual weight - Mean weight) / Standard deviation
Z-score = (24 - 26) / 3.6
Z-score ≈ -0.56
2. Find the area under the normal distribution curve corresponding to the Z-score using a Z-table or a statistical software. In this case, we need to find the area to the left of -0.56.
The same process is then repeated for the cat:
1. Calculate the Z-score for the weight of the cat:
Z-score = (Individual weight - Mean weight) / Standard deviation
Z-score = (19 - 10.5) / 1.9
Z-score ≈ 4.47
2. Find the area under the normal distribution curve corresponding to the Z-score using a Z-table or a statistical software. In this case, we need to find the area to the right of 4.47.
Once you've found the areas for both the dog and the cat, you can compare them. The animal with the larger area under the curve (either the dog or the cat) would weigh more in relation to its population.