Stats homework 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.

c) (i) Compute 𝑃(𝑋 < 240).

(ii) Draw a sketch to interpret your results.

(iii) Is this usual? Explain.

Answer 1

c)

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

Since probability is > 0.05 this is not an unusual value to obtain by chance.