Question

Before 2012, National Football League (NFL) football games that were tied at the end of regulation time continued after a coin toss. The team that won the coin toss could choose to receive the ball ir kick the ball. A whopping 98.1% of teams that won the coin toss chose to receive the ball. Between 1974 and 2011, there were 460 overtime games that did not end in a tie. Among those 460 games that decided were in overtime, 252 were won by the same team that won the overtime toss. Assume that wins and losses are equally likely, so both teams have the same 0.5 chance of winning the game in overtime.

Find the mean and standard deviation for the number of wins in groups of 460 games?

Answer 1

The values are provided in the question are as follows

x = total numbers of team won the toss = 252

n = total numbers of toss has been taken = 460

The mean for the number of wins in groups of 460 games is

p = x / n = 252 / 460 = 0.5478

Mean = p = 0.5478.......(1)

The standard deviation for the number of wins in groups of 460 games is

q = 1 - p = 1 - 0.5478 =

q = 0.4522

standard deviation =

=

standard deviation = 0.0232.......(2)

Summary

(1) Mean = 0.5478

(2) standard deviation = 0.0232