The amount of sales tax paid on a purchase is rounded to the nearest cent. Assume that the roundoff error is uniformly distributed in the interval -.5 to .5 cents.
a. Write the formula for the probability curve describing the round-off error.
b. Graph the probability curve describing the round-off error.
c. What is the probability that the round-off error exceeds .3 cents or is less than -.3 cents?
d. What is the probability that the round-off error exceeds .1 cent or is less than -.1 cent?
e. Find the mean and the standard deviation of the round-off error.
f. Find the probability that the round-off error will be within one standard deviation of the mean.