The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
What is the distribution of
¯
x
x
¯
?
¯
x
x
¯
~ N(,)
What is the distribution of
∑
x
∑
x
?
∑
x
∑
x
~ N(,)
P(
¯
x
x
¯
> 19.8214) =
Find the 60th percentile for the mean score for this sample size.
P(20.6214 <
¯
x
x
¯
< 23.2262) =
Q1 for the
¯
x
x
¯
distribution =
P(
∑
x
∑
x
> 829.0774) =
For part c) and e), is the assumption of normal necessary? NoYes