Answer:
17.205 miles
Step-by-step explanation:
Since these directions form a 90-degree angle, we can use the Pythagorean Theorem.
14^2 + 10^2 = c^2
196 + 100 = c^2
296 = c^2
It doesn't have a perfect square root, you can either say that it is or approximately 17.205 miles.
This result is approximate.
=========================================================
Explanation:
mu = 750 = mean
sigma = 75 = standard deviation
The raw scores or x values are x = 750 and x = 825
Let's compute the z score for each x value
z = (x - mu)/sigma
z = (750 - 750)/75
z = 0
and
z = (x - mu)/sigma
z = (825 - 750)/75
z = 1
Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.
Use a z score table to determine that
P(z ≤ 0) = 0.5
P(z ≤ 1) = 0.84314 approximately
So,
P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)
P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)
P(0 ≤ z ≤ 1) = 0.84314 - 0.5
P(0 ≤ z ≤ 1) = 0.34314 approximately
The value 0.34314 then converts to 34.314% which rounds to <u>34%</u>
Or you could use the empirical rule as shown below. The pink section on the right is marked <u>34%</u> which is approximate. This pink section is between z = 0 and z = 1.
