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 $430? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (b) What is the probability that the cost will be less than $280? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (c) What is the probability that the cost will be between $280 and $430? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (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.) $ Incorrect: Your answer is incorrect.

Answer 1

Solution :

Given that ,

mean = = 367

standard deviation = = 88

a) P(x > 430) = 1 - p( x< 430)

=1- p P[(x - ) / < (430 - 367) / 88]

=1- P(z < 0.72)

= 1 - 0.7642

= 0.2358

b) P(x < 280)

= P[(x - ) / < (280 - 367) / 88]

= P(z < -0.99)

Using z table,

= 0.1611

c) P(280 < x < 430) = P[(280 - 367)/ 88) < (x - ) /  < (430 - 367) / 88) ]

= P( -0.99 < z < 0.72)

= P(z < 0.72 ) - P(z < -0.99)

Using z table,

= 0.7642 - 0.1611

= 0.6031

d) Using standard normal table,

P(Z < z) = 5%

= P(Z < z ) = 0.05

= P(Z < -1.645 ) = 0.05  

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 88 + 367

x = $ 222