Assuming a normal distribution we find the standardized z scores for a:-

z1 = (80 - 180) / 25 = = -100/25 = -4
z2 = (280-180) / 25 = 4
Required P( -4 < z < 4) from the tables is >99.9%

b
z1 = 130-180 / 25 = -2
z2 = 230-180 / 25 = 2

from tables probability is 2* 0.4773 = 95.46 %

8 0

3 years ago

In baseball, the length of the path between each pair of consecutive bases is 90 feet. The paths form right angles. How far does

Tresset [83]

This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"

The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)

This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!

In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.

6 0

2 years ago