What formula do I use to find: a man that was shot out of a cannon, mean is 140 feet, stand. dev is 10, landing net is 28 feet long. how far away should the edge of the net be? I just need a push!
To find how far away the edge of the net should be, we can use the formula for z-score. The z-score formula is given as:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value you want to find the distance for (in this case, distance to the edge of the net)
- μ is the mean
- σ is the standard deviation
In this case, the mean (μ) is 140 feet and the standard deviation (σ) is 10 feet. We want to find the distance (x) to the edge of the net. Since the landing net is 28 feet long, the distance from the center to the edge of the net would be half of that, which is 14 feet. So, we can rewrite the formula as:
z = (x - 140) / 10
We can rearrange the formula to solve for x:
x = z * 10 + 140
Now, we need to find the z-score for the distance of 14 feet. To find the z-score, we use a z-table or a calculator that provides the z-score for a given probability. Assuming a normal distribution, the z-score corresponding to a distance of 14 feet can be found as:
z = (14 - 140) / 10 = -12.6
The negative sign indicates that the distance is below the mean.
Using the z-score of -12.6, we can substitute it back into the formula:
x = -12.6 * 10 + 140 = 17.4
Therefore, the edge of the net should be approximately 17.4 feet away from the launch point.