MBA5300: Data Analysis - Solar Power - Statistics Assignment Help

Assignment Task:

1. [30 Marks] Solar power has always been beneficial, and now it’s more accessible and  cost-effective. After 2 weeks advertisement, a survey asked a sample of 200 homeowners whether they want to install the solar energy system on their roof. Data  can be found in the Excel file AS2.XLSX (Solar). [20] 
If you randomly select a homeowner from this sample what is the probability that: a. The homeowner wants (Yes) to install solar system? 
b. His/her house is new? 
c. The homeowner agrees wants (Yes) to install solar system and His/her house is  new? 
d. A homeowner who does not want (No) to install solar system has a  townhouse? 
e. If you select a homeowner who lives in a single-family house, what is the  probability he wants (Yes) to install solar system?  
f. Are responses (Yes/No) and House Age (Year) independent events? 
2. [15 Marks] A fire alarm system inside grocery store has three types of activation  devices; P1, P2, and P3. When there is a fire, if one of the devices operates correctly, 
the fire alarm is turned on. In case of fire, the probability that P1 operates correctly is  0.98, the probability that P2 operates correctly is 0.95, and the probability that P3 operates correctly is 0.93. Assume the three activations devices operate independently  of each other. 
a. Find the probability that all activations devices will operate correctly. b. Find the probability that the alarm system will come on. 
c. Find the probability that the alarm system will fail. 
3. [35 Marks] A recent survey regarding online shopping shows customers’ purchase  when instant discount, free shipping, or no special offer were given. The probability  of the purchase is 8%, 6.5%, and 1.5% respectively. A sale manager offers free  shipping option to 30% and an instant discount to 20% of the customers. [25] 
a) Construct a probability tree for this experiment. 
b) What percent of customers who visit site did not make a purchase? c) If a customer makes a purchase, what is the probability that he/she had a offer  of free shipping? 
The sale manager also emailed three coupons, gold, silver, and green, to the equal  numbers of customers to see which one would lead to the highest probability of  purchase. Three months sale data shows increased probability of purchases; 2.5% for  gold, 4.1% for silver, and 3.7% for green coupons. 
d) Construct a probability tree for this experiment. 
e) What percent of customers who visited the site did make a purchase? f) What is the probability that a randomly selected customer has a silver coupon? 
4. [20 Marks] An insurance claim officer divided the clients into two groups, new license and experienced license drivers. He read the last year report that shows  11.25% of new drivers and 3.75% of experienced drivers are involved in an accident.  If 12% of drivers are new, find the following probabilities. For simplicity, assume 
year to year accident accidents for any driver are independent. (round your answers to  2 decimal places) 
a) What is the probability of accident for a driver?  
b) What is the probability that a new driver is involved in at least one accident  for 3 years?  
c) What is the probability of not having an accident for an experienced driver  for 3 years? 
d) The annual insurance premium is computed according to being involved to  at least one accident in 3 years. If an experienced driver pays $1000  premium, how much the premium of new drivers should be?  

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