SPEA-V 506: Statistical Analysis for Effective Decision Making - Statistics Assignment Help

Assignment Task:

Statistical Analysis for Effective Decision Making 

1. Assume that 52% of the population are Republicans and 48% of the population are Democrats. On a particular issue, 64% of Republicans are in favour and 52% of Democrats are in favour. If you randomly pick a person who is in favour of the issue, what is the probability that the person is a Democrat? 

2. Smoke and fire detectors are essential to save lives. Unfortunately, there are many false fire alarms. Suppose that the probability of an actual fire happening is very low at 5%. Smoke detectors are extremely good at detecting an actual fire, i.e., given a fire, there is a 99% probability that the smoke alarm detects it. If there is no fire, there is a 10% probability that the fire alarm sounds. Suppose that you hear a fire alarm, what is the probability that there is a fire? 

3. A friend has a coin and proposes the following gambling game. You will toss it 10 times and count the number of heads. The amount you win or lose on k heads is given by k² − 7 · k. 
(a) Plot the payoff function. 
(b) Make an exact computation using R to decide if this is a good bet. 
(c) Run a simulation and see that it approximates your computation in part (1). 

4. The probability of any O’Neill Air flight being delayed more than 15 minutes is 0.1. We randomly select four different O’Neill Air flights. 
(a) Calculate the probability that all four flights arrived within 15 minutes of the scheduled time? 
(b) Calculate the probability that none of the selected flights arrived within 15 minutes of the scheduled time? 
(c) Calculate the probability that at least one of the selected flights arrived within 15 minutes of the scheduled time? 

5. An apple juice company wants to purchase new bottling machines to fill 16-ounce cans. Two manufactures indicate the following performances for their machines. The first machine fills the cans with 16.5 ounces and a standard deviation of 0.3. The second machine fills the cans with 16.2 ounces and a standard deviation of 0.1. The filling quantities for both machines are normally distributed. Anything below 16 ounces cannot be sold since it does not meet the advertised 16 ounces. Which machine does the apple juice producer need to buy in order the minimize the number of cans which cannot be sold? 

6. Assume ACT scores are normally distributed with mean 19 and standard deviation of 4. A university accepts applicants which score in the top 20%. What is the minimum ACT score that gets you accepted? Calculate the probability of 0, 1, . . . , 10 students meetings the requirements out of 10 students. 

7. On average, a LED light bulb manufacturer produces 100 defective light bulbs out of 5,000. You randomly pick 8 light bulbs. What is the probability of finding 6 defective bulbs? 

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