Question 1084962: Q1)A NORMAL POPULATION HAS STANDARD DEVIATION OF 10. A RANDOM SAMPLE OF SIZE 25 HAS A MEAN OF 50. CONSTRUCT A 95% CONFIDENCE INTERVAL ESTMATE OF THE POPULATION MEAN.
Q2)THE ENVIRONMENTAL PROTECTION OFFICER OF A LARGE INDUSTRIAL PLANT SOUGHT TO DETERMINE THE MEAN DAILY AMOUNT OF SULPHUR OXIDE (POLLUTANT)EMMITED BY THE PLANT. BECAUSE MEASURMENTS COSTS WERE HIGH, ONLY A RANDOM SAMPLE 10 DAYS MEASURMENTS WERE OBTAINED : THESE WERE , IN TONS PER DAY.
8 7 10 15 11 5 8 5 13 12
SUPPOSE EMISSIONS PER DAY ARE NORMALLY DISTRIBUTED. ESTIMATED µ, THE MEAN AMOUNT OF SULPHUR OXIDES EMITTED PER DAY USING THE CONFIDENCE INTERVAL WITH A CONFIDENCE
COEFFICIENT OF 0.95
Q3)A RANDOM SAMPLE OF 400 MEMBERS OF LABOUR FORCE IN A FIVE STATE REGION SHOWED THAT 32 WERE UNEMPLOYED. CONSTRCT THE 95% CONFIDENCE INTERVAL FOR THE PROPORTION UNEMPLOYED IN THE REGION.
Q4)SUPPOSE THAT DURING ANY HOUR IN A LARGE DEPARTMENT STORE, THE AVERAGE NUMBER OF SHOPPERS IS 448 , WITH A STANDARD DEVIATION OF 21 SHOPPERS. WHAT IS THE PROBABILITY OF RANDOMLY SELECTING 49 DIFFERENT SHOPPING HOURS, COUNTING THE SHOPPERS, AND HAVING THE SAMPLE MEAN FALL BETWEEN 441 AND 446 SHOPPERS, INCLUSIVE/
zQ5)IF 10% OF A POPULATION OF PARTS IS DEFECTIVE, WHAT IS THE PROBABILITY OF RANDOMLY SELECTING 80 PARTS AND FINDING THAT 12 OR MORE ARE DEFECTIVE?
Q6)SUPPOSE THAT A POPULATIN PROPORTION IS , 40 AND THAT 80% OF THE TIME YOU DRAW A RANDOM SAMPLE FROM THIS POPULATION , YOU GET A SAMPLE PROPORTION OF 0.35 OR MORE. HOW LARGE A SAMPLE WERE YOU TAKING?
Q7)ASSUME THAT THE LENGTH OF TIME . X. BETWEEN CHARGES OF A CELLULAR PHONE IS NORMALLY DISTIBUTED WITH A MEAN OF 10 HOURS AND A STANDARD DEVIATON OF 1.5 HOURS. FIND THE PROBABILITY THAT THE CELL PHONE WILL LAST BETWEEN 8 AND 12 HOURS BETWEEN CHARGES.
Q8)SUPPOSE AN AUTOMOBILE MANUFACTURER INTRODUCES A NEW MODEL THAT HAS AN ADVERTISED MEAN IN CITY MILEAGE OF 27 MILES PER GALLON. ALTHOUGH SUCH ADVERTISEMENT SELDOM REPORT ANY MEASURE OF VARIABLILITY . SUPPOSE YOU WRITE THE MANUFACTURER FOR THE DETAILS OF THE TESTS, AND YOU FIND THAT THE STANDARD DEVIATION IS 3 MILES PER GALLON. THIS INFORMANTION LEADS YOU TO FORMULATE A PROBABILITY MODEL FOR THE RANDOM VARIABLE X , THE IN-CIY MILEAGE FOR THIS CAR MODEL . YOU BELIEVE THAT THE PROBABILITY DISTRIBUTION OF X CAN BE APPROXIMATED BY A NORMAL DISTRIBUTION WITH A MEAN OF 27 AND A STANDARD DEVIATION OF 3.
IF YOU WERE TO BUY THIS MODEL OF AUTOMOBILE, WHAT IS THE PROBABILITY THAT YOU WOULD PURCHASEDONE THAT AVERAGES LESS THAN 20 MILES PER GALLON FOR IN-CITY DRIVING? IN OTHER WORDS, FIND P(X<20).
SUPPOSE YOU PURCHASE ONE OF THESE NEW MODELS AND IT DOES GET LESS THAN 20 MILES PER GALLON FOR IN-CITY DRIVING. SHOULD YOU CONCLUDE THAT YOUR PROBABILITY MODEL IS INCORRECT?
Answer by ikleyn(52873)   (Show Source):
You can put this solution on YOUR website! .
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