Question

using excel and it's functions

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. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
3. Find the 80^th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

Answer 1

This is a normal distribution question with

X ~ N(250, 50)
a) P(x < 220.0)=?
The z-score at x = 220.0 is,

z = -0.6
This implies that


b) Given in the question
P(X < x) = 0.8
This implies that
P(Z < 0.8416) = 0.8
With the help of formula for z, we can say that

x = 292.0811

PS: you have to refer z score table to find the final probabilities.
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