Dave the jogger runs the same route every day (about 2.2 miles)

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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.