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 questions 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 vour cost?

Answer 1

c) The probability that the cost will be between S250 and S450 We have to find P (250 SX S 450) P (250 SX 450) P (-13295 S Zs 0.9432) 0)-P (0 = P (-1.3295 Z 0.4082+0.3264 Z 0.9432) [From Normal table] P (250 SX S 450) 0.7346 d) The cost for car repair is in the lower 5% automobile repair charge, then cost is We have given P(X<Xi)-0.05, thus we have to find the value ofXi Now, P(X < X) = 0.05 P (Z< Z1) 0.05 [From Normal table] P(Z1 SZ S0) 0.05 0)-0.45 0.5 (Z1 Z From the normal probability table the corresponding value of Z1 for the probability 0.45 is -1.645 Therefore, Z1--1645 (X1-p)=-1645 x-3672--1.645 Xi = (-1.645)*88+367=-144.76 + 367 = 222.24 Thus the cost is $222.24