Instructions: Do not round until final answer. Provide diagrams for normal distribution and proper probability notation. Show all formulas, work, and provide proper notation and/or units for full marks.

1) Electric Light tested a sample of 20 lightbulbs which produced a mean lifetime of 114 hours with a standard deviation of 4.7 hours. Construct 98% confidence interval for the true mean lifetime of the lightbulbs.

2) A previous study of professional baseball players showed that the standard deviation of home runs hit by players who play a full season was 7.23 homeruns. If researchers want to conduct a new study to determine the number of homeruns a player hits in a year, how many players would they need in their study if they want to be within 1.5 home runs of the true mean? Use a 95% level of confidence?

3) A high school's basketball team's points per game total is normally distributed with a mean score of 67.4 points with a standard deviation of 8.75 points. In a random game that the team plays, what is the probability that the team will score:

a) Over 75 points? (5 marks)

b) Over 55 points? (5 marks)

c) Between 75 and 82 points? (5 marks)

4) A local restaurant wants to determine what proportion of their customers prefer red wine with dinner instead of white wine. If they use a 99% level of confidence, how many customers do they need to survey to be within 2.5% of the true proportion?

5) A sample of 80 households in a neigbourhood of St. Catharines produced a mean property tax of $4117.89 per year with a standard deviation of $324.72. Construct a 92% confidence interval for the true mean property tax for that neighbourhood of St. Catharines.

6) The finish times for a 10 km race were normally distributed with a mean time of 44.5 minutes with a standard deviation of 3.83 minutes. What time separates the fastest 15% of runners who completed the race?

7) A professional hockey researcher wants to determine the true proportion of people who think fighting should not be part of the game. After surveying 800 fans at a hockey game the survey found that 212 people think fighting should not be part of the game. Construct a 90% confidence interval for the true proportion.