Reference no: EM132391557
1. 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.
2. On the ballot, Illinois voters had the option to select "yes" or "No" when asked if the state's minimum wage should be increased from $8.25 to $10 an hour by January 1, 2015. Before the actual voting date, a survey with a sample size of 50 found that 61.75% percent of respondents supported the minimum wage.
a) Calculate the 95% and 90% confidence intervals for the minimum wage vote.
b) After the election, the results of vote turned out that 62% percent voters answered "yes". Do the confidence intervals include the true mean?
c) If the true support rate is 0.6175, what is the sample size should be if we allow 0.05 of margin of error at 95% confidence level?