In a regular NBA season, each team plays 82 games, some at home and some on the road. Can you afford the price of a ticket? The Web site wiki.answers.com indicates that the low prices are around $10 for the high up seats while the court-side seats are around $2000 to $5000 per game and that the average price of a ticket is $75.50 a game. Suppose that we test this claim by selecting a random sample of n = 50 ticket purchases from a computer database and find that the average ticket price is $82.50 with a standard deviation of $75.25.
a. Do you think that x, the price of an individual regular season ticket, has a mound-shaped distribution? If not, what shape would you expect?
b. If the distribution of the ticket prices is not normal, you can still use the standard normal distribution to construct a confidence interval for µ, the average price of a ticket. Why?
c. Construct a 95% confidence interval for µ, the average price of a ticket. Does this confidence interval cause you support or question the claimed average price of $75.50? Explain.