Question

Here is a summary of the Boston Marathon completion times for two years.

Year
Mean (minutes)
Standard deviation (minutes)
Number of runners
2012
263
50
21,576
31,984
2014
243
52
A sports journalist takes separate random samples of 35 runners from each year. Then they look at the
difference in the mean completion time sampled from each year 2012 - 2014).
What do we know about the shape of the sampling distribution of D2012 22014, and why?

Answer 1

"It's approximately normal, because both sample sizes are at least 30."

Explanation:

The shape of the population distribution is unknown; however as the sample size is 35 (fulfills the sample size criteria:
`\geq` 30), we can conclude that the sampling distribution is therefore approximately normal.