Question

suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 246 feet and a standard deviation of 39 feet. a. find the probability that a randomly hit fly ball travels less than 200 feet. select b. if someone hits 800 fly balls, how many will travel further than 300 feet? select

Explanation:

Step1: Calculate z-score for 200 ft

$z = \frac{X - \mu}{\sigma} = \frac{200 - 246}{39} \approx -1.18$

Step2: Find $P(Z < -1.18)$

Using standard normal table, $P(Z < -1.18) \approx 0.1190$

Step3: Calculate z-score for 300 ft

$z = \frac{300 - 246}{39} \approx 1.38$

Step4: Find $P(Z > 1.38)$

$P(Z > 1.38) = 1 - P(Z < 1.38) \approx 1 - 0.9162 = 0.0838$

Step5: Compute number of fly balls

$\text{Number} = 800 \times 0.0838 \approx 67$

Answer:

A. 0.1190
B. 67