I just need to know what formula I need to use to get started on this equation: A man that was shot out of a cannon and the mean is 140 feet, stand. dev. is 10, landing net is 28 feet long. To maximize the peron's probability of landing on the net, how far away from the cannon should he be position the nearest edge of the net?
I know the answer is 126 but I cannot figure out how to get it. Could some get me started on this? Thanks!
To solve this problem, you can use the concept of normal distribution and z-scores.
First, let's define the random variable X as the distance of the man from the cannon to the nearest edge of the net. The mean of X is given as 140 feet, and the standard deviation as 10 feet.
To maximize the probability of landing on the net, we want to find the distance from the cannon that corresponds to the point where the z-score is zero. This means it is exactly at the mean of the distribution.
We can use the formula for z-score:
z = (x - μ) / σ
Where:
- x is the actual value of the variable
- μ is the mean
- σ is the standard deviation
In our case, we want to find the value of x when z is zero, which corresponds to the mean:
0 = (x - 140) / 10
Now, we can solve for x:
0 = x - 140
x = 140
So, the distance from the cannon to the nearest edge of the net should be 140 feet to maximize the person's probability of landing on the net.
However, in the question, you mentioned the answer is 126 feet. It is possible that there is additional information or context that was not provided, which may affect the final answer.