As a manager of a shop, you have an access to the past sales data, which indicates that the daily average sales is $800 with the standard deviation $120. Suppose the breakeven sales target of this month is $10,000 and there are 16 business days for the shop on this month. Then, the probability that the sales break even can be approximated by 

[Q17 – Q23] Let Y be a random variable with probability density function , for . Answer the following questions. Show your work for all questions.

Find the value of c. Provide 4 digits after the decimal point.

What is the probability that a patient is given a placebo given she says the pain is reduced? Provide three digits after the decimal point.

[Q6 – Q10] Choose the distribution best models each of the following statistical phenomena.

The number of times you should call to order a pizza delivery until someone picks up the phone on the Super Bowl night.

The total scores that Georgia Tech football team scored in all of the games in the past five football seasons.

A pop-up coffee stand charges $3 per cup of coffee they sell.  The daily demand (in number of cups sold) has mean 200 and standard deviation of 20. The cost of daily operation is $200. Compute the following. mean of the daily profit = [a] standard deviation of the daily profit = [b] 

Compute Var(Y). Provide 4 digits after the decimal point.

Suppose X and Y are independent, what is the standard deviation of 2X – Y + 2? Provide 4 digits after the decimal point.