An automobile insurer has found that repair claims have a mean of $920 and a standard deviation of $870. Suppose that the next 100 claims can be regarded as a random sample from the long-run claims process.


(a) Find the mean and the standard deviation of the sampling distribution for the sample mean.


(b) Find the margin of error for an 80% confidence interval


(C) Find 80% confidence interval for the mean claim amount for a sample of 100 claims. you may leave your answer in form.


(D)If the insurer would like to minimize the variability in the sample mean, what can she/he do?


Question 2: A local county has a very active adult education venue. A random sample of the population showed that 189 out of 400 persons 16 years old or older participated in some type of formal adult education activities, such as basic skills training, apprenticeships, personal interest courses, and part-time college or university degree programs.


Assume the variable is normally distributed


(a) State the parameter our confidence interval will estimate.


(b) Identify the conditions that must be met to use this procedure and explain how you know that each one has been satisfied.


(c) Find the point estimate and the margin of error for a 98% confidence interval.


(d) Estimate the true proportion of adults participating in some kind of formal education program with 98% confidence. State your answer in the context of the setting