Q.A company is producing a product that its size has a normal distribution with mean of 7 and std of 0.1. A product that has a size of is called a standard product. Producing a standard product has 1250 profit. If a product is smaller than 6.91 it is not useable and will result in 1050 $ of negative profit. If the product is bigger than 7.09, producer will be able to fix it and make it as a standard product by spending 200$. Calculate the expected profit for producing a product.

Q.A random sample consisting of 200 business executives working in the Downtown area is drawn and they were asked to answer a set of questions. One question in the survey asked about their annual salary and another about their annual expenses on luxury goods. We regress the spending on salary, and the regression has R2 = 0.884.

a. Interpret the result of the R2 value in this context.

b. "Despite the high value of R2, a linear regression model may not be appropriate."Comment.

Q.Given certain level of significance, what is the relationship between the confidence interval and size of the sample? Explain the answer.