Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of
0 and a standard deviation of 1. Find the probability that a given score is less than 1.99 and draw a sketch of the region.
1 answer:
Answer:
Step-by-step explanation:
To find this probability, we shall be using the z-score route
Mathematically ;
z-score = (x -mean)/SD
From the question, x = 1.99, mean = 0 and SD = 1
So z = (1.99-0)/1 = 1.99
So the probability we want to calculate is;
P(z<1.99)
This value can be obtained from the standard normal distribution table.
P(z < 1.99) = 0.9767
The sketch of the region is as shown as in the attachment.
You might be interested in
Any rhombus is a parallelogram, but not the other way around. If you were to make a Venn Diagram, the "rhombus" portion is entirely inside the set of "parallelograms".
The same can be said about rectangles as well. Any rectangle is a parallelogram, but not the other way around.
If we overlapped the region of rectangles and rhombuses, then we form the region for squares. A square is a combination of a rhombus and a rectangle.
Any square has all four sides the same length (property of a rhombus) and all angles equal to 90 (property of a rectangle). Since a square inherits properties of a rectangle and rhombus, it automatically makes any square a parallelogram.
Check out the venn diagram below.
