A density curve like an inverted letter "V" The first segment goes from the point (0, .6) to the point (0.5, 1.4). The second segment goes from (.05, 1.4) to (1, .6)
Find the percent of the observations that lie below .3
I have no idea how to do this If you could tell that would be great I got this
.3(.6) + 2^-1 .3 h = area
were h is the height of the triangle bit
.18 + .15 h = area
h is the height of the triangle part
also note that in other problems I was asked to find the median and stuff and check my answer in the back and it told me I was right the median is at .5
The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inche. What percent of the dowels have a diameter greater than 0.57?
To find the percent of observations that lie below 0.3 in the given density curve, you can follow these steps:
1. Visualize the two segments of the inverted "V" shape on a graph with the given coordinates:
- The first segment goes from the point (0, 0.6) to the point (0.5, 1.4).
- The second segment goes from the point (0.05, 1.4) to the point (1, 0.6).
2. Calculate the area below the density curve until the point x = 0.3:
- The area under the first segment (triangle) can be found using the formula for the area of a triangle:
Area of triangle = (base * height) / 2
The base of the triangle is 0.5 - 0 = 0.5, and the height is 1.4 - 0.6 = 0.8.
So, the area of the triangle is (0.5 * 0.8) / 2 = 0.2.
- The area under the second segment (rectangle) can be found by calculating the area of a rectangle:
Area of rectangle = length * width
The length of the rectangle is 1 - 0.05 = 0.95, and the width is 0.6 - 0.6 = 0 (since it's a straight line).
So, the area of the rectangle is 0.95 * 0 = 0.
- Therefore, the total area below x = 0.3 is 0.2 + 0 = 0.2.
3. Calculate the percentage of observations that lie below 0.3:
To find the percentage, multiply the total area by 100:
Percentage = Total area * 100
Percentage = 0.2 * 100 = 20%.
So, the percent of the observations that lie below 0.3 in the given density curve is 20%.