Question

Consider observations of the number of wins per season by National Football League teams over the years 1989-2008. The observed mean is 8 wins/season and the observed standard deviation is 3.02. A histogram illustrates these data.

Referring to these NFL data and assuming normality, the probability that a randomly chosen team wins 11 or more games is?

Group of answer choices

a. 0.16

b. 0.25

c. None of these options

d. 0.09

e. 0.37

Answer 1

The number of wins per season by national football league teams is observed.

The number of wins per season is normally distributed with mean 8 wins and standard deviation of 3.02.

Let, X be the random variable denoting the number of wins by a randomly selected team.

Then, as given, X follows normal with mean 8 and standard deviation of 3.02.

So, Z=(X-8)/3.02 follows standard normal (0,1).

To find the chance that a randomly selected team wins 11 or more games.

ie. to find P(X>=11)

=

=

=

=

=

=

Where Z is the standard normal variate.

=

=

Where, phi is the distribution function of the standard normal variate.

=1-0.8389 from standard normal table

=0.1611

which is approximately 0.16.

So, the correct answer is (a) 0.16.