Question 1If 100 random samples of size n were drawn and if for each a 99% confidence interval for ? was computed then exactly 99 of these confidence intervals would contain the true population mean within their limits. Elaborate.Question 2Assuming the population variance is known and then if the sample size is doubled the variance of the distribution of the sample mean of the random variable would be halved. ExplainQuestion 3How does Z the standard normal distribution variable relate to the standard deviation of its distributionQuestion 4It is desired to test the claim that a steady diet of a medicine will cause a male to lose 10 lbs over 5 months. A random sample of 49 males was taken yielding an average weight loss over 5 months of 12.5 pounds with s = 7 lbs. a. Identify the critical value suitable for conducting a two-tail test of the hypothesis at the 2% level.b.Is there any significant evidence that the pharmaceutical company claim about the drug performance is not valid given an ?=0.02? Show your work.