Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

1.    If X = distance in feet for a fly ball, then X ~ _____(_____,_____) ?

2.    Find the z-scores for fly balls that travel 200 feet and 300 feet.

3.    What is the approximate percentage of fly balls that travel between 200 and 300 feet? (Use Empirical Rule)

4.    Find the z-score for a fly ball that travels 150 feet.

5.    What is the approximate percentage of fly balls that travel fewer than 150 feet? (Use Empirical Rule)

6.    What is the approximate percentage of fly balls that travel more than 200 feet? (Use Empirical Rule)

7.    99.7% of fly balls travel between what two distances? (Use Empirical Rule)

8.    What is the percentage of fly balls that travel more than the mean distance? (Use Empirical Rule)

9.    What is the z-score for a fly ball that travels 270 feet?

10. What fly ball distance has z-score of -1.30?

Answer 1

1)

2)


3)

4)

5)

6)

7)
99.7% lie within 3 S.D. of Mean according to Empirical formula

99.7% lie within 100 and 400;

8)
50% are more than Mean as distribution is symmetrical with respect to Mean.

9)

10)