Question

are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of Row Total 436 5 46 59 Less Than 1 Year 1-2 Years 3-4 Years 5-9 Years 10-14 Years 15 or More Years East 57 59 112 77 99 Midwest 120 62 172 South 94 158 100 West Column Total 468 291 What is the probability that a customer chosen at random has the following characteristics? (Enter your answers as fractions.) (a) has been loyal 10 to 14 years 291/2004 527 (b) has been loyal 10 to 14 years, given that he or she is from the Eas 771430 he Eas (c) has been loyal at least 10 years ** 10 year (d) has been loyal at least 10 years, given that he or she is from the West (e) is from the West, given that he or she has been loyal less than 1 () is from the South, given that he or she has been loyal less than 1 y (9) has been loyal 1 or more years, given that he or she is from th (h) has been loyal 1 or more years, given that he or she is from the We (1) Are the events from the East and loyal 15 or more years independent? Explain No. Ployal 15 or more years). Ployal 15 or more years | East). No. There events cannot occur together Yes. These events can occur together Yes. Ployal 15 or more years) - Ployal 15 or more years East).

Answer 1

6 llogal to bo 14 yrs ) - P(logal 10 to 14 yrs & from east) from east PG from east) 7/2004 436 2004 - 77/436) © Pl lobyal atleast 10 yrs) = (291+527)/2004 - |818/2004] Dpr logal atleast 10 yrs). Pllogal atleast 10 YRS4 from west) from west 7 Plfrom west) - (45+91)/2004 - 1136/355 | 355/2004 @ pl from west . P(from west & loyal less than I YR logal less than 1 yo) Plloral less than & YR) - 41/2004 1411571 157/2004 6 pl from south P(from south & Loyal less thant YR) logal less than 1 Yo) - Pllogal less than I YR) 53/2004 3/157 157/2004 Pl loyal I or more YR) Plfrom east & loyal for more TR) from east f e l from east) (57+59 +1{2+77+99)/20041404 4436/2004 p/logal for more YR)- P(from west & Loyal for more PR) M from west Pc from west) (33+67+78+45+91)/2004 - 314355 355/2004 © P(loyal 15 or more PRB) = 527/2004 Plloyal 15 or more yes | East)= 99/436 No, Plloyal 15 or more yos) # Piloyal 15 or more YR | East) - 436