Question

The average score for games played in the NFL is 22.4 and the standard deviation is 9.3 points. 46 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

P(∑x∑x < 1046.1872)

Answer 1

Solution:

Given in the question

Average score for grades played = 22.4

Population standard deviation = 9.3

No. Of sample = 46 games

sample = 1046.1872

Sample average Xbar= 1046.1872/46 = 22.7432

We need to calculate

P(Xbar<22.7432) = ?

We will be using normal distribution, so z score can be calculated as

Z-score = (Xbar-)//sqrt(n) = (22.7432-22.4)/9.3/sqrt(46) = 0.2503

So from Z table we found p-value

P(Xbar<22.7432) = 0.5988

And P(Sum(X) <1046.1872) = 0.5988