Consider the following population:

U.S. Census data showing expenditures on maintenance and repairs (in millions of USD) performed by businesses in the year 2020 in the sate of NY with the following mean, median and standard deviation:

Mean = $20,500

Median = $23,400

Standard deviation = $8,300

Instructions:

(3 points) If you select samples of size n = 5 from the population described above, describe the shape and properties of the sampling distribution of sample means, X

(3 points) If you select samples of n = 250 from the population described above, describe the shape and properties of the sampling distribution of sample means, X

(2 points) If you select a random sample of size n=100, what is the probability that the sample mean will be less than $19,000?

(2 points) Calculate and interpret the 90% confidence interval for the population mean of all NY state expenditures on maintenance and repairs. Consider sample size n = 200.

Use and present answers with 4 decimals.