The average score for games played in the NFL is 20.5 and the standard deviation is 9.3 points. 44 games are randomly selected. Round all probabilities to 4 decimal places where possible, percentiles to 2 decimal places and assume a normal distribution.
a.) What is the distribution of x? ~ N( ,)
b.) P(x < 20.697) =
c.) Find the 75th percentile for the mean score for this sample size.
d.) P(18.697 < x < 22.101) =
e.) Is the assumption of normal necessary for this problem? Yes No