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) = 

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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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Question

10-According to Harper’s Index, 60% of all federal inmates are serving time for

drug dealing. A random sample of 16 federal inmates is selected.

(a) What is the probability that 8 or more are serving time for drug dealing? (Round your answer to three decimal places.)

(b) What is the probability that 5 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)

(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)

_______________________________________________________________________________________________________________________________

15-

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 10.3 minutes and a standard deviation of 2.0 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

__________________________________________________________________________________________________________________________________

16-

Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 10.75 hours with a standard deviation of 3.5 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

(a) Find the probability that with heavy use, the battery life exceeds 11 hours. (Round your answer to four decimal places.)

(b) You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone? (Round your answer to the nearest tenth of an hour.)

hours   

_____________________________________________________________________________________________________________________________________

17-

The University of Montana ski team has thirteen entrants in a men’s downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the thirteen team entrants achieve first, second, and third places?

 

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