PURCHASE BEHAVIOUR REGARDING PLASMA-SCREEN TELEVISION AND DVR ARE GIVEN BELOW: PURCHASED DVR PURCHASED PLASMA SCREEN YES NO TOTAL PLASMA SCREEN 38 42 80 NOT PLASMA SCREEN 70 150 220 TOTAL 108 192 300 a. Find the probability that if a household that purchased a big screen television is randomly selected, the television purchased is a plasma screen. b. Find the probability that a randomly selected household that purchased a big-screen television also purchased a plasma screen television and a DVR c. Find the probability that among households that purchased a big screen television, they purchased a plasma- screen television or a DVR. d. If a household purchased a plasma- screen television, what is the probability that it also purchased a DVR? e. Use decision tree to find the probability that a household purchased a DVR, given that the household purchased a plasma screen television. 2. The amount of time consumed by an individual at a bank ATM is found to be normally distributed with mean = 160 seconds and standard deviation = 50 seconds. i.) What is the probability that a randomly selected individual will consume less than 80 seconds at the ATM. ii.) What is the probability that a randomly selected individual will spend between 3 minutes and 4 minutes at the ATM. iii.) What is the probability that a randomly selected individual will spend between 140 seconds and 175 seconds at the ATM. iv.) What is the probability that a randomly selected individual will spend between 1 minute and 2 minutes at the ATM. v.) Within what length of time do 25% of individuals complete their job at the ATM. vi.) What is the least amount of time required for individuals with top 8% of required time? 3. The performance Measurement Group collected data on the rates of correctly filled electronic orders by industry. Assume a sample of 700 electronic orders provided the following results. Order Pharmacy Consumer Computers Telecommunication Correct 207 136 151 178 Incorrect 3 4 9 12 Test whether order fulfillment is independent of the industry (take = 0.05), which industry has the highest percentage of correctly filled orders