the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1.       Tesla Battery Recharge Time. The electric-vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle’s battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between 90 and 120 minutes.

a.       Give a mathematical expression for the probability density function of battery recharging time for this scenario. (Hint: recall that a is the lower number and b is the larger number).

b.      What is the probability that the recharge time will be less than 110 minutes?

c.       What is the probability that the recharge time required is at least 100 minutes?

d.      What is the probability that the recharge time required is between 95 and 110 minutes?

e.       What is the expect value of the recharge time required?

f.       What is the standard deviation of the recharge time required? (Hint: Use Standard deviation = Square root of (b-a)2/12).

 

NORMAL DISTRIBUTION PROBLEM

1.      Automobile Repair Costs. Automobile repair costs in the U.S. state of Georgia continue to rise with the average cost now at $ 402.66 per repair (U.S. News & World Report website). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $75. Answer the following questions about the cost of automobile repairs in Georgia.

a.       What is the probability that the cost will be more than $500?

b.      What is the probability that the cost will be less than $300?

c.       What is the probability that the cost will be between $300 and $500?

d.      If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?

 

 

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