Consider the record of field goal percentages (%FGM) made in the NFL over a seas
ID: 3154302 • Letter: C
Question
Consider the record of field goal percentages (%FGM) made in the NFL over a season (256 games). League-wide, the average %FGM was 85%. The below histogram presents the number of teams and their percentage made (that is 2 teams were 65-70%, one team 70-75%, etc.
If you were to take a random sample of 10 games and record % FG made of this 10 game sample and then repeat this sample 25 times (with replacement), the distribution of the 25 sample %FGM would:
1) Be skewed towards the low values.
2) Be skewed towards the higher values.
3) Be normally distributed about the league average 85 %.
4) Would be centered at a value higher than 85% because 3 teams were lousy kickers.
Explanation / Answer
How ever the sample be,but when we repeat the sampling n number of times,then the mean of the samples follow a normal distribution. THis is said by central limit theorem.
Hence as the average FG is 85%
The distribution of the 25 sample % FGM would be normally distributed about the league average 85%