# Tutor profile: Kane T.

## Questions

### Subject: Microeconomics

If the price of coke decreases and then in turn the demand for pepsi decreases, what type of products are coke and pepsi?

In this case coke and pepsi would be substitutes. If the price of one substitute decreases the demand for the other product will decrease as consumers will demand the lower cost options in the case of substitute products.

### Subject: Calculus

What is the integral of the function f(x) = 2x^3 - y with respect to x?

We integrate with respect to x and therefor will get an answer of x^4/2 -xy.

### Subject: Statistics

What is the 95% confidence interval for a distribution with mean of 30, standard deviation of 2, and sample size of 120?

A 95% confidence interval is created by finding the interval in which 95% of our values are within. We first compute the standard error: standard deviation/sqrt(sample size) = 2/sqrt(120) = .1826. We then multiple the standard error by 1.96 (which is the amount of standard deviations needed for 95% of the data). 1.96 * .1826 = .3579. We then subtract and add this number to the mean to get our bounds. [30 - .3579, 30 + .3579] = [29.6421 , 30.3579] is our 95% confidence interval.

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