Question

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 ques- tions about the cost of automobile repairs. a. What is the probability that the cost will be more than $450? b. What is the probability that the cost will be less than $250? c. What is the probability that the cost will be between $250 and $450? d. If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?

Answer 1

Answer:

$\mu = 367$

$\sigma = 88$

a. What is the probability that the cost will be more than $450?

We are supposed to find P(x > 450)

Formula : $z=\frac{x-\mu}{\sigma}$

$z=\frac{450-367}{88}$

$z=0.9431$

Refer the z table :

P(z<0.9431)=0.8264

P(z> 0.9431)=1-P(z<0.9431)=1- 0.8264= 0.1736

Hence the probability that the cost will be more than $450 is 0.1736

b)What is the probability that the cost will be less than $250?

We are supposed to find P(x<250)

Formula : $z=\frac{x-\mu}{\sigma}$

$z=\frac{250-367}{88}$

$z=-1.3295$

Refer the z table :

P(z<-1.3295)=0.0934

Hence the probability that the cost will be less than $250 is 0.0934

c)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 =0.733

Hence the probability that the cost will be between $250 and $450 is 0.733

d)  If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?

p = 0.05

refer the z table

z = -1.65

Formula : $z=\frac{x-\mu}{\sigma}$

$-1.65=\frac{x-367}{88}$

$-1.65 \times 88=x-367$

$-145.2+367=x$

$221.8=x$

Hence If the cost for your car repair is in the lower 5% of automobile repair charges, so, cost is $221.8