Research and evaluation 1 Res/341?

Question

6. The mean of a normal distribution is 400 pounds. The
standard deviation is 10 pounds.

a. What is the area between 415 pounds and the mean of
400 pounds?
b. What is the area between the mean and 395 pounds?
c. What is the probability of selecting a value at
random and discovering it has a value of less than
395 pounds?

Answer 1

Hi,
Well, by far the easiest way to do this is with a TI-83 Plus, TI-84 or equivalent graphing calculator. But since people on this website tend not to use graphing calculators, I’ll show you how to do it by hand first.
a. What is the area between 415 pounds and the mean of
400 pounds?
z=(x-x-bar)/σ (Where I’ve used x-bar for the mean.)
z=(415-400)/10
z=1.5
From the tables for a normal distribution the area is”
0.4332.

b. What is the area between the mean and 395 pounds?
z=(395-400)/10
z=-0.5
From the tables for a normal distribution the area is”
0.1915.

c. What is the probability of selecting a value at
random and discovering it has a value of less than
395 pounds?
Just subtract the area in b) above from 0.5, the total area below the mean.
.5-0.1915=0.3085

Just in case you might want to use a graphing calculator, here’s how.
Part a)
a) Press 2ND, DIST (the VARS key), and press 2 to paste normalcdf( to the home screen.
b) Enter data according to this syntax: normalcdf(lower bound, upper bound, mean, std.def). Part a) will look like this:
normalcdf(400, 415, 400, 10)
c) Press ENTER and the area will be displayed.

Part b)
Press 2ND ENTRY( the ENTER key, and edit the entry so it looks like this:
normalcdf(385, 400, 400, 10). Press ENTER and the answer will be displayed.

Part c)
Press 2ND ENTRY( the ENTER key, and edit the entry so it looks like this:
normalcdf(-1E9, 395, 400, 10). Press ENTER and the answer will be displayed. (Make sure the symbol is the negative sign, (-), not the minus sign. The “E” is obtained by pressing 2ND and the comma key.

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