Question 1:
A sample of 500 respondents was selected in a large city area to determine information concerning consumer behavior. There are 260 female selected for the study. 360 of the respondents are found to enjoy shopping for clothing and 136 of them are males.
a) Suppose the respondent chosen is a female. What, then, is the probability that she does not enjoy shopping for clothing?
b) Suppose the respondent chosen enjoys shopping for clothing. What, then, is the probability that the individual is a male?
c) Are enjoying shopping for clothing and the gender of the individual statistically independent? Explain.
Question 2
Many researchers have developed models based on financial ratios that predict whether or not a company will go bankrupt in the next year. In a test of one such model, the model correctly predicted bankruptcy for 85% of firms if they in fact did fail and it correctly predicted non-bankruptcy for 82% of firms given that they did not fail. Suppose that the model maintains the same reliability when applied to a new group of 100 firms, of which four fail in the year following the time at which the model makes its predictions.
a) Determine the number of firms for which the model's prediction will prove to be correct.
b) Find the probability that the model makes an incorrect prediction.
c) Find the probability that one of these firms will fail, given that the model has predicted it will go bankrupt.
d) Find the probability that one of these firms will not fail, given that the model has predicted it will go bankrupt.