Good Morning Sirs , I was doing an inference for Single Population Mean and i got stuck in getting to the root of the problem, is it possible to help me get there?

1. It has been suggested that an investment portfolio selected by randomly throwing darts at the stock market page of the Wall Street Journal may be a sound investment. Suppose that you own such a portfolio of 19 stocks randomly selected from all stocks listed on the Jamaica Stock Exchange (JSE). On a certain day, the average stock rose by 3.0 points. Assume that stock price movements are normally distributed with a mean 3.0 points and standard deviation 3 points. What is the probability that your portfolio decreased in price? 2. A random sample of 150 students was taken to estimate the mean monthly rent paid by the whole student population. Assume that the standard deviation of monthly rents from this sample is $500. a) What is the standard error of the sample mean monthly rent? b) What is the probability that the sample mean exceeds the population mean by more than $50? c) What is the probability that the sample mean differs from the population mean by more than $30? The Kendle Company is interested in estimating the average amount of money that consumers spend on Kendle books annually. A random sample of 81 Kendle users reported that they spent an average of $300 with a standard deviation of $50. a) Construct a 95% confidence interval to estimate the annual average expenditure on Kendle books. b) What is the margin of error of for this interval? ECON2008 Lecture Exercises - Week 7 4. A company that produces plastic sheets would like to show that a new kind of plastic has an average stress resistance that is greater than 30 pounds per square inch. A random sample of plastic sheets is selected for this test. Using the output below, One-Sample Statistics Std. Error Mean Std. Deviation Mean Data 12 30.2083 2.41415 69690 a) conduct the appropriate hypothesis test. You may use the fact that a 2-tailed p-value = 0.771 b) construct a 90% confidence interval for the average stress resistance per square inch