Stats hw please help

Question

Suppose the average 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. We randomly sample 49 fly balls. Let 𝑋~(𝜇𝑥̅ , 𝜎𝑥̅ ) where 𝑋 = the average distance for 49 fly balls.

d) Compute 𝑃(𝑋 < 240)

(e) Find the 80th percentile of the distribution of the average of the 49 fly balls.

Answer 1

d)

P(x < 240)

Transform to z score = (sample mean - population mean)/(standard deviation(std)/sample size^0.5)

P(z < (240-250)/(50/49^0.5)

P(z < -1.4) = 0.0808

e)

z-score corresponding to 80th percentile is 0.842

0.842 = (sample mean - 250)/(50/49^0.5)

6.014 = sample mean - 250

256.014 = sample mean for 80th percentile