Problem 2.
THE PROBABILITY THAT A RANDOMLY CHOSEN SALES PROSPECT WILL MAKE A PURCHASE IS 0.20. IF A SALESMAN CALLS ON SIX PROSPECTS,
A. WHAT IS THE PROBABILITY THAT HE WILL MAKE EXACTLY FOUR SALES?
B. WHAT IS THE PROBABILITY THAT THE SALESMAN WILL MAKE FOUR OR MORE SALES?
C. WHAT IS THE EXPECTED NUMBER OF SALES (AS A LONG-RUN AVERAGE) AND THE VARIANCE ASSOCIATED WITH MAKING CALLS ON 15 PROSPECTS?
Problem 3.
THE NUMBER OF TRUCKS ARRIVING HOURLY AT A WAREHOUSE FACILITY HAS BEEN FOUND TO FOLLOW THE PROBABILITY DISTRIBUTION IN TABLE BELOW. CALCULATE
NUMBER OF TRUCKS ( X ) 0.00 1.00 2.00 3.00 4.00 5.00 6.00
PROBABILITY [P( X )] 0.05 0.10 0.15 0.25 0.30 0.10 0.05
A. THE EXPECTED NUMBER OF ARRIVALS X PER HOUR AND
B. THE VARIANCE OF THIS PROBABILITY DISTRIBUTION FOR THE DISCRETE RANDOM VARIABLE.
Problem 4.
A MAIL-ORDER FIRM HAS A CIRCULAR WHICH ELICITS A 10 % RESPONSE RATE. SUPPOSE 20 OF THE CIRCULARS ARE MAILED AS A MARKET TEST IN A NEW GEOGRAPHIC AREA. ASSUMING THAT THE 10% RESPONSE RATE IS APPLICABLE IN THE NEW AREA, DETERMINE THE PROBABILITIES OF THE FOLLOWING EVENTS:
A. NO ONE RESPONDS
B. A MAJORITY OF THE PEOPLE RESPOND
C. WHAT IS THE EXPECTED NUMBER OF PEOPLE WILL RESPOND?
Problem 5.
THE MAXIMUM NUMBER OF CUSTOMERS ARRIVING DURING RANDOMLY CHOSEN 10-MIN INTERVALS IS 5 AT A DRIVE-IN FACILITY SPECIALIZING IN PHOTO DEVELOPMENT AND FILM SALES. IT HAS BEEN FOUND THE NUMBER OF ACTUAL SALES MADE FOLLOWS THE PROBABILITY DISTRIBUTION IN TABLE BELOW.
NUMBER OF SALES ( X ) 0 1 2 3 4 5
PROBABILITY [P( X )] 0.15 0.25 0.25 ? 0.10 0.05
A. PLEASE FILL IN THE MISSING PROBABILITY FOR X=3 IN THE TABLE ABOVE (CELL WITH “?” MARK)
B. CALCULATE THE EXPECTED NUMBER AND VARIANCE OF ARRIVALS IN 10-MIN INTERVAL.
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