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.
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?