Hi i need your help to solve the following

6. Suppose the distribution of the heights of 18-year old men in the United States is approximately Normal with unknown mean ? and known standard deviation ? = 2.8 inches. A simple random sample of size 36 from this population yields a sample mean of 69.4 inches.

(a) (3 pts) Give a 95% confidence interval for the mean height of 18-year old men in the United States.

(b) (2 pts) Interpret this interval.

(c) (2 pt) Without doing any further calculations, explain what would happen to the width of the interval above if the confidence level were changed to 90%.

(d) (2 pts) How many 18-year old men must we sample if we want to estimate the mean height ? within a margin of error of 0.4 inches with 95% confidence?

(e) (1 pt) What is the critical value (z*) for a confidence level of 97.5%?

7. The distribution of the heights of adults in the United States is bimodal (i.e., has two peaks).

(a)(2pts) If a sample of 2000 adults were selected, would the sampling distribution of the sample mean be approximately Normal? Why or why not?

(b)(2pts) If the sample size were increased, would the sampling variability increase, decrease, or stay the same? Explain your answer.

8. (2 pts) The mean salary of employees at Cost-U-Less is $32,722. A random sample of 22 employees had a mean of $31,963. Which number is a parameter and which number is a statistic?

A Markov chain with state space S = {0, +1, +2, 13, .. } and transition probabilities specified by Pi,i+1 = p, Pli-1 = 1 - p, where 0