You observe an Olympic Athlete in the long-jump. Suppose the distance of each ju

Question

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 variance ?2. 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

Calculate an unbiased estimate for the value of ?

Calculate an unbiased estimate for the value of ?2?

c. Construct an interval that has a 95% probability of containing ?.

The athlete says that he is better than Carl Lewis, who jumped an average distance

of 8.50 throughout his career. What would you say to that?

Suppose both of your guesses from parts a.) and b.) are exactly correct. What is the

probability that the athlete

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

Explanation / Answer

1. mean=8.67125

2. variance= (8.5-8.67)^2 + (8.84-8.67)^2+(8.32-8.67)^2 +(8.72-8.67)^2 + (8.49-8.67)^2 +(8.79-8.67)^2 +(8.87-8.67)^2 +(8.82-8.67)^2

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