In the 2010-11 season, the mean number of penalty minutes for the 30 teams of the National Hockey League (NHL) was 12.20

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In the 2010-11 season, the mean number of penalty minutes for
the 30 teams of the National Hockey League (NHL) was 12.20 minutes,
with a standard deviation of 2.25 minutes. Assume that the 2010-11
season is a representative sample of all teams in all seasons.
(a) State whether, with explanation, the sample size is large
enough for the CLT to hold.
(b) Describe the shape, center and standard error of a sampling
distribution based on this sample.
(c) What is the value of the degrees of freedom, df, for this
sample?
(d) Find and interpret a 99% confidence interval for the mean
number of penalty minutes in the NHL.
(e) Does the data provide sufficient evidence at a 1% level that
the mean number of penalty minutes in the NHL is less than 13
minutes? Show all details of the test and provide a conclusion in
context.