Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News & World Report website, January 5, 2015). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. Answer the following questions about the cost of automobile repairs. What is the probability that the cost will be more than $450? What is the probability that the cost will be less than $250? What is the probability that the cost will be between $250 and $450? If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?

Answer:[tex]\mu = 367[/tex][tex]\sigma = 88[/tex]a. What is the probability that the cost will be more than $450?We are supposed to find P(x > 450)Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex] [tex]z=\frac{450-367}{88}[/tex] [tex]z=0.9431[/tex]Refer the z table :P(z<0.9431)=0.8264P(z> 0.9431)=1-P(z<0.9431)=1- 0.8264= 0.1736Hence the probability that the cost will be more than $450 is 0.1736b)What is the probability that the cost will be less than $250?We are supposed to find P(x<250)Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex] [tex]z=\frac{250-367}{88}[/tex] [tex]z=-1.3295[/tex]Refer the z table :P(z<-1.3295)=0.0934Hence the probability that the cost will be less than $250 is 0.0934c)What is the probability that the cost will be between $250 and $450?P(250<z<450)=P(z<450)-P(z<250) = 0.8264 - 0.0934 =0.733Hence the probability that the cost will be between $250 and $450 is 0.733d)  If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost? p = 0.05refer the z table z = -1.65Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex] [tex]-1.65=\frac{x-367}{88}[/tex] [tex]-1.65 \times 88=x-367[/tex] [tex]-145.2+367=x[/tex] [tex]221.8=x[/tex]Hence If the cost for your car repair is in the lower 5% of automobile repair charges, so, cost is $221.8