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You observe an Olympic Athlete in the long-jump. Suppose the distance of each jump is a random variable that follows a normal distribution with mean and variance2. He jumps 8 times and records the following distances.
Jump Distance (meters)
1 8.79
2 8.87
3 8.82
4 8.49
5 8.74
6 8.32
7 8.84
8 8.50
a. Calculate an unbiased estimate for the value of ?
b. Calculate an unbiased estimate for the value of ?2?
c. Construct an interval that has a 95% probability of containing ?.
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