In a recent season, the population standard deviation of the yards per carry for all running backs was 1.241.24. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed.
1.81.8
4.54.5
7.47.4
5.85.8
5.35.3
3.33.3
3.93.9
6.26.2
2.92.9
2.52.5
2.72.7
5.85.8
3.73.7
3.23.2
3.63.6
6.76.7
6.96.9
3.43.4
4.64.6
7.37.3
6.56.5
6.56.5
5.15.1
2.62.6
3.93.9
Which distribution should be used to construct the confidence interval?
T distribution
To determine the distribution that should be used to construct the confidence interval, we need to consider the sample size and the assumption of the population distribution.
In this case, the sample size is 25, which is relatively small. When the sample size is small, it is not appropriate to assume a normal distribution unless the population distribution is known or can be approximated as normal.
Given that the question states "Assume the yards per carry are normally distributed," we can conclude that the appropriate distribution to construct the confidence interval is the normal distribution.