Question

You may need to use the appropriate appendix table to answer this question.

Automobile repair costs continue to rise with the average cost now at $367 per repair.† 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.

(a)

What is the probability that the cost will be more than $450? (Round your answer to four decimal places.)

(b)

What is the probability that the cost will be less than $230? (Round your answer to four decimal places.)

(c)

What is the probability that the cost will be between $230 and $450? (Round your answer to four decimal places.)

(d)

If the cost for your car repair is in the lower 5% of automobile repair charges, what is your maximum possible cost in dollars? (Round your answer to the nearest cent.)

$

Answer 1

Solution :

(a)

P(x >$450 ) = 1 - P(x < 450)

= 1 - P[(x - ) / < (450 - 367) / 88)

= 1 - P(z < 0.94)

= 1 - 0.8264

= 0.1736

Probability = 0.1736

(b)

P(x < $230) = P[(x - ) / < (230 - 367) / 88]

= P(z < -1.56)

= 0.0594

Probability = 0.0594

(c)

P($230 < x < $450) = P[(230 - 367)/ 88) < (x - ) /  < (450 - 367) / 88) ]

= P(-1.56 < z < 0.94)

= P(z < 0.94) - P(z < -1.56)

= 0.8264 - 0.0594

= 0.767

Probability = 0.767

(d)

Using standard normal table,

P(Z < z) = 5%

P(Z < -1.65) = 0.05

z = -1.65

Using z-score formula,

x = z * +

x = -1.65 * 88 + 367 = 222

maximum possible cost in $222