Answer:
Step-by-step explanation:
To find the probability that a randomly selected test taker scored below 50, we need to first of all determine the z-score of 50.
The z-score for a normal distribution is given by:
.
From the question, the mean score is , the standard deviation is, , and the test score is .
We substitute these values into the formula to get:
We now read the area that corresponds to a z-score of -1.33 from the standard normal distribution table.
From the table, a z-score of -1.33 corresponds to and area of 0.09176.
Therefore the probability that a randomly selected test taker scored below 50 is
We have the system of equations:
y=1/3x+5
y=2/3x+5
To solve it graphically, we need to graph both lines and see in which point the lines intersect.
You can see the graph below, and you can see that the lines intersect in the point (0, 5)
Now, we can also solve this analytically.
We can use the fact that for the solution, we need y = y.
Then we can write:
(1/3)*x + 5 = (2/3)*x + 5
First, we can subtract 5 in both equations to get:
(1/3)*x = (2/3)*x
This only has a solution when x = 0.
Replacing x = 0 in one of the equations, we get:
y = (1/3)*0 + 5 = 5
Then the solution is x = 0, and y = 5, as we already could see in the graph.
There are 34 composite numbers between 1 to 50 which are as follows: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50.