The Brooklyn District Attorney's office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to "Benford's law," which applies in this case. Among 784 checks issued by a suspect company, there were none with amounts that had a leading digit of 1.
a. If there is a 30.1% chance that the leading digit of the check amount is 1, what is the expected number of checks among 784 that should have a leading digit of 1?
b. Assume that groups of 784 checks are randomly selected. Find the mean and standard deviation for the numbers of checks with amounts having a leading digit of 1.
c. Use the results from part (b) and the range rule of thumb to identify the values that are significantly low.
d. Given that the 784 actual check amounts had no leading digits of 1, is there very strong evidence that the suspect checks are very different from the expected results? Why or why not?