Answer:
[tex]2.95\times10^{-5}[/tex]
Step-by-step explanation:
a)The pressure level that will trigger a warning is
30 - 30*0.28 = 21.6 psi
b) The probability that the TPMS will trigger warning at 21.6 psi, given that tire pressure has a normal distribution with average of 30 psi and standard deviation of 2 psi is:
[tex]f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}[/tex]
where x = 21.6, μ = 30 and σ = 2
[tex]f(22.94)={\frac {1}{2 {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {21.6-30}{2 }}\right)^{2}}[/tex]
[tex]f(22.94)=0.2e^{-8.82} = 2.95\times10^{-5}[/tex]
