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Answer:
If the task is performed in less than or equal to 130.8 seconds, then, the individuals qualify for advanced training.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 150 sec
Standard Deviation, σ = 15 sec
We are given that the distribution of time taken is a bell shaped distribution that is a normal distribution.
Formula:
We have to find the value of x such that the probability is 0.10
P(X < x)
Calculation the value from standard normal z table, we have,
Thus, if the task is performed in less than or equal to 130.8 seconds, then, the individuals qualify for advanced training.
The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:
So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
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