1. A random draw lottery has sold $52 000 000 worth of tickets, with each ticket...

 

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1. A random draw lottery has sold $52 000 000 worth of tickets, with each ticket sold for $5.00. The prizes and their frequencies are shown in the following table. a) Copy and complete this table using a spreadsheet. /3TI P(x) x*P(x) Prize ($), x Number of Prizes 12 000 000 206 955 2 408 1 5 25 147 100 100 1000 10 5000 b) What is the random variable, X, for this distribution? c) Is this a uniform probability distribution? Why or why not? d) What is the expected profit per ticket for the lottery corporation? E(X) /1APP /1APP /1APP 2. At the Toyota plant in Cambridge, an assembly line robot installs media players in each car produced on the line. For quality control, the units are tested to make sure they are installed properly. The probability of a malfunction is 0.2. (Spreadsheet work is not required for this question.) a) Define the random variable, X. /1APP b) Determine the probability that 5 media players will be tested before a malfunction is found. Express the answer in percentage to 1 decimal place. 12APP c) What is the expected number of tests before a malfunction is found? /1APP 3. A bag contains six red marbles, five yellow marbles, and four black marbles. Marbles are selected from the bag, one at a time, without replacement, until four marbles have been taken. a) Using a spreadsheet, create a probability distribution table for choosing red marbles. Show calculations within the table. /3TI b) Using a spreadsheet, graph the distribution. c) Determine the expected number of red marbles. /2COM /1APP 1. A random draw lottery has sold $52 000 000 worth of tickets, with each ticket sold for $5.00. The prizes and their frequencies are shown in the following table. a) Copy and complete this table using a spreadsheet. /3TI P(x) x*P(x) Prize ($), x Number of Prizes 12 000 000 206 955 2 408 1 5 25 147 100 100 1000 10 5000 b) What is the random variable, X, for this distribution? c) Is this a uniform probability distribution? Why or why not? d) What is the expected profit per ticket for the lottery corporation? E(X) /1APP /1APP /1APP 2. At the Toyota plant in Cambridge, an assembly line robot installs media players in each car produced on the line. For quality control, the units are tested to make sure they are installed properly. The probability of a malfunction is 0.2. (Spreadsheet work is not required for this question.) a) Define the random variable, X. /1APP b) Determine the probability that 5 media players will be tested before a malfunction is found. Express the answer in percentage to 1 decimal place. 12APP c) What is the expected number of tests before a malfunction is found? /1APP 3. A bag contains six red marbles, five yellow marbles, and four black marbles. Marbles are selected from the bag, one at a time, without replacement, until four marbles have been taken. a) Using a spreadsheet, create a probability distribution table for choosing red marbles. Show calculations within the table. /3TI b) Using a spreadsheet, graph the distribution. c) Determine the expected number of red marbles. /2COM /1APP