Q1)According to a local business research, the hourly wage of workers in NY state follows a normal distribution with a standard deviation of $5.00, and a mean $23.00.

A) What is the probability that a randomly selected NY resident has an hourly wage greater than $25.00?

B) What is the probability that the average of 6 randomly selected NY residents is greater than $25.00?

C) What is the probability that all of the 6 people in the randomly selected sample have an hourly wage greater than $25.00?

Q2)Assume that a researcher wants to collect data to make inference about the hourly wage in New Paltz area. The hourly wage in New Paltz area also follows a normal distribution and the standard deviation is also $5.

A) What will be the required sample size, if the researcher wants to achieve a desired margin of error at $1.00 at the significant level of 95%.

B) What will be the required sample size, if the researcher wants to achieve a desired margin of error at $1.00 at the significant level of 98%.

C) If the researcher collects the following data of the hourly wage,

17.318.625.719.828.512.618.316.2

what's the 95% confidence interval for the population mean estimation?

Is the hourly wage in New Paltz area significantly different from the state average level, at 95% confidence level?

D) Based on the previous data, what is the value of the test statistic if the researcher wants to test whether the New Paltz average hourly wage isgreaterthan $17? What is the P-value of this test? What is your conclusion regarding the test at 95% significant level?