SOLUTION: Good morning everyone, I am really having a hard time to figure this out without using calculator.Any help is appreciated! Q: Suppose that the distance of fly balls hit to th

Question 1002005: Good morning everyone,
I am really having a hard time to figure this out without using calculator.Any help is appreciated!
Q: 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.
a. 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.
I put it in calculator normalcdf (-10^99, 220, 250,50) = 0.27425
I looked at the book but the book calculated z score first and used normal table. z= (220-250)/50 = -0.6
Area to the left of -0.6 = 0.5 � 0.22575 = 0.27425 <- Not sure where this comes from.....???
So the probability that this ball traveled fewer than 220 feet is 0.27425.

The answer is the same but I am not sure how to come up with the answer without using calculator....
Thanks in advance!!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you don't want to use a calculator, then you must use a table. There is no other way to do this type of problem. It's nearly impossible to do by hand because it takes a very long time unless you're a human calculator.

I recommend a table like this one. Your stats textbook most likely has something like this in the back of the book. This table is the list of areas to the left of given z scores.

Note: some tables give areas to the right of z-scores so be careful how the table is set up. Read all the instructions for the table.

You have the correct z-score. It is z = -0.6

Look at the table. For this table I'm showing, you need to go to the row that starts with "-0.6" (towards the bottom of page 1). Then go to the column that has ".00" at the top. In this case, column 1. The intersection of the "-0.6" row and ".00" column has the number 0.27425 in that cell

Recall that this table shows areas under the standard normal curve that are to the left of a given z score. The given z-score of -0.6 corresponds to the area of 0.27425

So that's another way to find the answer of 0.27425
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