Question

Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning?

Answer 1

Answer:

0.0075

Step-by-step explanation:

According to the given situation, the calculation of the probability that the TPMS will trigger a warning is shown below:-

The tire pressure which is 26% below the target pressure is

$= 26\% \times 28$

= 7.28

Therefore, Tire pressure monitoring systems warn at below is

= 28 - 7.28

= 20.72

Now we will assume tire pressure be x

So,

$P(X<20.72) = P(\frac{X-\mu}{\sigma}<\frac{20.72-28}{3} )$

After solving the above equation we will get

= $P(X<20.72) = P(Z<-2.43)$

we will get

= 0.0075