In: Statistics and Probability
Suppose that the distance, X, 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 60 fly balls. What is the 70th percentile of the distribution of sample means? |
Given that,
mean = = 250
standard deviation = = 50
n = 60
= 250
= / n = 50/60=6.45
Using standard normal table,
P(Z < z) = 70%
= P(Z < z) = 0.70
z = 0.52 Using standard normal table,
Using z-score formula
= z * +
= 0.52*6.45+250
= 253.35