Question

20 -In a sales effectiveness seminar, a group of sales representatives tried two approaches to selling a

customer a new automobile: the aggressive approach and the passive approach. For 1160 customers, the following record was kept:

Sale No Sale Row Total

Aggressive 253 327 580

Passive 477 103 580

Column Total 730 430 1160

Suppose a customer is selected at random from the 1160 participating customers. Let us use the following notation for events: A = aggressive approach, Pa = passive approach, S = sale, N = no sale. So, P(A) is the probability that an aggressive approach was used, and so on.

(a) Compute P(S), P(S | A), and P(S | Pa). (Enter your answers as fractions.)

P(S) =

P(S | A) =

P(S | Pa) =

(b) Are the events S = sale and Pa = passive approach independent? Explain.

Yes. The two events can occur together. No. The two events cannot occur together.   Yes. P(S) = P(S | Pa). No. P(S) ≠ P(S | Pa).

(c) Compute P(A and S) and P(Pa and S). (Enter your answers as fractions.)

P(A and S) =

P(Pa and S) =

(d) Compute P(N) and P(N | A). (Enter your answers as fractions.)

P(N) =

P(N | A) =

(e) Are the events N = no sale and A aggressive approach independent? Explain.

Yes. The two events can occur together. Yes. P(N) = P(N | A).   No. P(N) ≠ P(N | A). No. The two events cannot occur together.

(f) Compute P(A or S). (Enter your answer as a fraction.)

P(A or S) = 

_______________________________________________________________________________________________________________________

19-

A recent study gave the information shown in the table about ages of children receiving toys. The percentages represent all toys sold.

Age (years) Percentage of Toys

2 and under 20%

3-5 17%

6-9 29%

10-12 13&

13 and over 21%

What is the probability that a toy is purchased for someone in the following age ranges?

(a) 6 years old or older

%

(b) 12 years old or younger

%

(c) between 6 and 12 years old

%

(d) between 3 and 9 years old

%

A child between 10 and 12 years old looks at this probability distribution and asks, “Why are people more likely to buy toys for kids older than I am (13 and over) than for kids in my age group (10-12)?” How would you respond?

__________ The 13-and-older category may include children up to 17 or 18 years old. This is a larger category.

__________ The 13-and-older category may include children up to 17 or 18 years old. This is a smaller category.

 

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