Reference no: EM132391556

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1. According to the stock index, the return from January 2014 to December 2014 shows the average of 7% with standard deviation of 2.5%. 

a) According to the Central Limit Theorem (CLT), what the sample mean distribution if we randomly pick 25 stocks?

b) What is the probability that the sample mean is higher than 8% if we randomly select 25 stocks?

c) What is the probability that the sample mean is lower than 6.5% if we randomly select 100 stocks?

d) Suppose the population mean is unknown, but we know the population standard deviation is 2.5. What is the 95% confidence interval of population mean if the sample mean is 7.2$ and the sample standard deviation is 3% from randomly selected 25 stocks? 

e) Suppose the population mean and the population standard deviation are unknown. What is the 95% confidence interval of population mean if the sample mean is 7.2$ and the sample standard deviation is 3 from randomly selected 25 stocks? 

2. The  medicaldegree.com reported  the medical doctors'  salary level. The mean salary for the doctor is $250,000 and standard deviation of $100,000. Find the following probabilities assuming that doctor's salary has a normal distribution.  

a) What is the probability that the doctor's salary is higher than $500,000?

b) What is the probability that the doctor's salary is less than $100,000?

c) Suppose we randomly select 36 doctors, what is the probability that the sample mean of doctor's salary is less than $225,000.

d) Suppose we don't have any information about population, and from a sample of 100 doctors, we find the sample mean salary was $255,000 with the standard deviation of $99,500. What is the 95% confidence interval?  

e) Based on the standard deviation of $100,000 and allow the margin of errors to $20,000, what is your sample size should be at 95% confidence level.