Lecture 3 Numerical Descriptive Measures 统计学 作业三.docx

Tutorial 3_Numerical Descriptive distributionQuestion 1:The Credit card companies are increasing their revenue by raising the late fees charged to their customers. According to a study by , late fees represent the third largest revenue source for card companies after interest charges and payments from the merchants who accept their cards. In a recent year, 58% of all credit card customers had to pay a late fee (Ron Lieber, “Credit-Card Firm Collect Record Levels of Late Fees,”The wall Street Journal, May 21, 2002, D1).If a random sample of 20 credit card holders is selected, what is the probability thatzero had to pay a late fee?no more than 5 had to pay a late fee?more than 10 had to pay a late fee?what assumptions did you have to make to answer (a) through (c)?Answer:Customers paying the last fee or not should be independent. So, according to the question, the number of 20 customers who pay the last fee is X ～B(20 ,0.58)According toformula: a. P(X=0)=b. P(X=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=P(Xc.P(X10)=P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)==0.171+0.177+0.150+0.104+0.057+0.025+0.008+0.002+2.688P(X10)=0.6943d. Because that customers paying the last fee or not should be independent, the question satisfy the condition of binomial distribution, so use the formula can calculate each data.Question 2:For e-commerce merchants, getting a customer to visit a web isn’t enough. Merchants must also persuade online shoppers to spend money by completing a purchase. Experts at Andersen Consulting estimated that 88% of web shoppers abandon their virtual shopping carts before completing their transaction (Rebecca Quick, “The Lessons Learned”, The wall street Journal, April 17, 2006, R6). Consider a sample of 20 customers who visit an e-commerce Web site, and assume that the probability a customer will leave the site before completing a transaction is 0.88. Use the binomial model to answer the following questions:What is the expected value,