Considering the given probability distribution, we have that there is a 0.349 = 34.9% probability that the left tire has a pressure of at least 25 psi.
<h3>What is the probability distribution?</h3>
The probability distribution for the air pressure of the tires of the car(X right, Y left) is given as follows:
- f(x,y) = K(x² + y²), 18 ≤ x ≤ 28, 18 ≤ y ≤ 28.
The pressure in the right tire is found to be 22 psi, hence y = 22 and:
- f(x,y) = K(x² + 484), 18 ≤ x ≤ 28.
The value of K is found considering that the <u>sum of all probabilities has to be 1</u>, hence:
Applying the Fundamental Theorem of Calculus:
7317.33K + 13552K - 8712K - 1944K = 1
10213.33K = 1
K = 1/10213.33
K = 0.000098.
The probability that the left tire has a pressure of at least 25 psi is:
0.349 = 34.9% probability that the left tire has a pressure of at least 25 psi.
More can be learned about probabilities at brainly.com/question/14398287
#SPJ1