Question

The Dynamic Credit Company issues credit cards and uses software to detect fraud. After tracking the spending habits of one customer, it is found that charges over $100 constitute 35.8% of the credit transactions. Among 30 charges made this month, 18 involve totals that exceed $100. Does this constitute an unusual spending pattern that should be verified? Explain.

Answer 1

Pr(charges over $ 100) = 35. 8% = 0.358

Here for the given sample

sample proportion p^ = 18/30 = 0.6

Here to be unusual spending patter, the sample proportion must be outside 2 standard deviation from population proportion.

Here standard error of proporton =sqrt [0.358 * (1 - 0.358)/30] = 0.0875

Here Z value of he sample proportion

Z = (0.6 - 0.358)/ 0.0875 = 2.766

so here to acheive such kind of spending in the given month, the probability is only 1 - Pr(Z < 2.766) = 0.0028

so that is something unusual here that should be verified vigilantly.