Rocky Hill Bikes (RHB) manufactures high-end bicycles. Rocky Hill's vice-president of finance asked you to investigate the warranty expense for RHB's dual-suspension hybrid bike. You sampled 600 warranty claims and found that the average warranty expense per bike appeared to be normally distributed with an average of $53 (to your surprise, every bike in your sample had a warranty expense). You may assume that the standard deviation is $9. Assuming the normal distribution is an accurate probability model, answer the following questions:
a. What is the probability that a randomly selected warranty expense for these dual suspension hybrid bikes would be less than $38?
b. What is the probability that a randomly selected warranty expense for these bikes would be between $38 and $62?
c. Your boss has reminded you that RHB loses money on these bikes when the warranty expense exceeds $68.What is the probability that a randomly selected warranty expense for these bikes would be above $68?