Micron Technology has sales offices located in four cities: Dallas, Seattle, Bos
ID: 3204648 • Letter: M
Question
Micron Technology has sales offices located in four cities: Dallas, Seattle, Boston, and Los Angeles. An analysis of the company’s accounts receivables reveals the number of overdue invoices by days, as shown here. Days Overdue Dallas Seattle Boston Los Angeles Under 30 days 137 122 198 287 30-60 days 85 46 76 109 61-90 days 33 27 55 48 Over 90 days 18 32 45 66 Assume the invoices are stored and managed from a central database. a) What is the probability that a randomly selected invoice from the database is from the Boston sales office? b) What is the probability that a randomly selected invoice from the database is between 30 and 90 days overdue? c) What is the probability that a randomly selected invoice from the database is over 90 days old and from the Seattle office? d) If a randomly selected invoice is from the Los Angeles office, what is the probability that it is 60 days or fewer days overdue? e) Is the event 30-60 days overdue independent of the Boston Office? Explain.
Explanation / Answer
a) probability that a randomly selected invoice from the database is from the Boston sales office =374/1384
=0.270231
b)bility that a randomly selected invoice from the database is between 30 and 90 days overdue =316/1384
=0.228324
c) probability that a randomly selected invoice from the database is over 90 days old and from the Seattle office =32/1384 =0.02312
d) probability that it is 60 days or fewer days overdue if given its is from the Los Angeles office=(287+109)/510
=0.776471
e)probabilty of event 30-60 days P(A) =316/1384 =0.228324
and probabilty of event from boston =374/1384 =0.270231
also probabilty of from boston and 30-60 days overdue P(AnB) =76/1384 =0.054913
as P(AnB) is not equal to P(A).P(B)
hence they are not independent
days overdue dallas Seattle Boston Los Angeles Total <30 137 122 198 287 744 30-60 85 46 76 109 316 61-90 33 27 55 48 163 >90 18 32 45 66 161 Total 273 227 374 510 1384