Question

1.       A local electronics retailer recently conducted a study on purchasers of large screen televisions. The study recorded the type of television and the credit account balance of the customer at the time of purchase. They obtained the following results.

Credit Balance	Standard TV	LCD	Plasma	Projection
Under $200	13	13	40	5
$200-$800	9	10	23	14
Over $800	16	14	15	32

Construct a totals row and column for the table (as I did in several videos). Then answer the following questions:

a.       What is the probability of a customer having a credit balance of less than $200 (5 pts.)

b.       What is the probability of randomly selecting a customer who purchased a Standard TV and had a credit balance of under $200? (5 pts.)

c.       What is the probability of randomly selecting a customer who purchased an LCD or Plasma TV? (5 pts.)

d.       What is the probability of randomly selecting a customer who purchased a Plasma TV? (5 pts.)

e.       What is the probability of randomly choosing a customer who purchased a Plasma TV given that they had a credit balance of more than $800? (15 pts.)

f.        Are the two variables shown in this table, credit balance and type of TV purchased, statistically independent? Please provide a mathematical justification for your answer. (15 pts.)

Answer 1

Credit Balance	Standard TV	LCD	Plasma	Projection	total
Under $200	13	13	40	5	71
$200-$800	9	10	23	14	56
Over $800	16	14	15	32	77
total	38	37	78	51	204

a)

  probability of a customer having a credit balance of less than $200 =71/204

b)

probability of randomly selecting a customer who purchased a Standard TV and had a credit balance of under $200 =13/204

c)

probability of randomly selecting a customer who purchased an LCD or Plasma TV=(37+78)/204

=115/204

d)

probability of randomly selecting a customer who purchased a Plasma TV =78/204

e)probability of randomly choosing a customer who purchased a Plasma TV given that they had a credit balance of more than $800 =15/77

f)

as probability of randomly choosing a customer who purchased a Plasma TV given that they had a credit balance of more than $800 is not equal to probability of randomly selecting a customer who purchased a Plasma TV ; therefore variaables credit balance and type of TV purchased are not statistically independent