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 $490? (Round your answer to four decimal places.)

(b) What is the probability that the cost will be less than $290? (Round your answer to four decimal places.)

(c) What is the probability that the cost will be between $290 and $490? (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 :

Given that ,

mean = = $367

standard deviation = = $88

(a)

P(x > $490) = 1 - P(x < 490)

= 1 - P((x - ) / < (490 - 367) / 88)

= 1 - P(z < 1.3977)

= 1 - 0.9189

= 0.0811

Probability = 0.0811

(b)

P(x < $290) = P((x - ) / < (290 - 367) / 88)

= P(z < -0.875)

= 0.1908

Probability = 0.1908

(c)

P($290 < x < $490) = P((290 - 367)/ 88) < (x - ) / < (490 - 367) / 88) )

= P(-0.875 < z < 1.3977)

= P(z < 1.3977) - P(z < -0.875)

= 0.9189 - 0.1908

= 0.7281

Probability = 0.7281

(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 = 221.8 = 222

maximum possible cost in dollars $222