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Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News & World Report website, Jan

uary 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?

1 answer:

babunello [11.8K]2 months ago

4 0

Reply:

$\mu = 367$

$\sigma = 88$

a. What is the likelihood that the cost will exceed $450?

We need to determine P(x > 450)

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

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

$z=0.9431$

Consult the z table:

P(z<0.9431)=0.8264

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

Therefore, the probability that the repair costs will surpass $450 is 0.1736

b)What is the likelihood that the repair cost is below $250?

We need to establish P(x<250)

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

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

$z=-1.3295$

Referencing the z table:

P(z<-1.3295)=0.0934

Hence, the probability that the cost will be under $250 is 0.0934

c)What is the likelihood that the repair cost is in the range of $250 and $450?

P(250<z>

Therefore, the likelihood that the repair costs will fall between $250 and $450 is 0.733

d) If your car repair expense ranks in the lowest 5% of all automobile repair costs, what would your payment be?

p = 0.05

checking against the z table

z = -1.65

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

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

$-1.65 \times 88=x-367$

$-145.2+367=x$

$221.8=x$

Thus, if your repair price falls within the lowest 5% of car repair costs, the amount charged would be $221.8

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