Dave the jogger runs the same route every day (about 2.2 miles). On 18 consecutive days, he recorded the number of steps using a pedometer. The results were

3,450	3,363	3,228	3,360	3,304	3,407	3,324	3,365	3,290
3,289	3,346	3,252	3,237	3,210	3,140	3,220	3,103	3,129

a) Construct a 95% confidence interval for the true mean number of steps Dave takes on his run.(Round your answers to 4 decimal places.)

b)What sample size would be needed to obtain an error of 20 steps with 95% confidence?(Enter your answer as a whole number (no decimals). Use a z-value taken to three decimal places in your calculations.)

SHOW THE WORK IF POSSIBLE. I know the mean is 3278.7222 and the standard deviation is 97.0535.