Question 3: [10 Marks]

It's been estimated by the national health authority of Mexico that on average the Mexican adults drink 18 cans of Coca-Cola a week which causes a drastic increase in diabetes and high blood pressure among them. A recent survey conducted by an NGO indicates that on average the daily consumption of Coca-Cola by a Mexican adult is 2.7 with a total standard deviation of 3.3 cans and 60 degrees of freedom.

1. Using a 97.5% confidence level and P-value approach can you conclude that the Mexican adult's average weekly consumption of Coca-Cola is more than 18 cans?
2. Determine a 97.5% confidence interval for the corresponding population mean.

Question 4: [5 Marks]

In the car industry, Toyota and Nissan have an old rivalry in terms of mileage and performance. In order to beat Toyota, the R&D team of Nissan has implemented a new technology that enabled them to increase the mileage while reducing the carbon emission of Nissan X-Trail. The new version of the Nissan X-Trail Hybrid car has promised to provide an average of 40 miles per gallon (mpg) of gas. However, the gas mileage varies from car to car due to a variety of conditions, driving styles, and other factors and has been reported to be as high as 55 mpg. Let's, assume that the distribution of miles per gallon for Nissan X-trail hybrid cars has a mean of 30 mpg and a standard deviation of 4.5 mpg. Find the probability that the average miles per gallon for a sample of 50 Nissan X-trail hybrid cars is-

1. Less than 42
2. Between 38 and 43
3. Less than the population mean by 3 or more.

Question 5: [5 Marks]

Company 'x' wants to enter into the market with a new detergent powder. Before launching their product, they conducted a survey where they found that 85% of the people who tried their product were satisfied with it. Due to this high satisfaction rate, the company decided to launch its detergent powder. During a certain month, 85 customers bought this new detergent powder. Find the probability that of these 85 customers, the number of consumers who are satisfied is-

1. 62 or fewer
2. At least 68
3. Exactly 65