SOLUTION: Let us assume that from a population with mean μ=100 and standard deviation σ=15 a sample random variable of n=900 is selected. What

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Question 1183700: Let us assume that from a population with mean μ=100 and standard
deviation σ=15 a sample random variable of n=900 is selected.

What is the probability P(X ≤ 101.1)?
What is the probability P(X ≥ 101.5)?
What is the probability P(99.3 < X ≤ 100.5)?

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
For normal distributions, consider < and ≤ the same. Also consider > and ≥
the same.

Let us assume that from a population with mean μ=100 and standard
deviation σ=15 a sample random variable of n=900 is selected.

What is the probability P(X ≤ 101.1)? 
On your TI-84, 
press 2ND 
press VARS
press 2

Make the screen read: 

    normalcdf
lower:-9999999
upper:101.1
μ:100
σ:15/√(900)        <---the square root key is 2ND x2
Paste

Scroll down with the down arrow to Paste

Read on the screen

normalcdf(-9999999,101.1,100,15/√(900))

Press ENTER

Read 0.9860966011, round to 0.9861
What is the probability P(X ≥ 101.5)?
 

As above but make the screen read

    normalcdf
lower:101.5
upper:99999999
μ:100
σ:15/√(900)     
Paste

Answer:  0.0013499672, round to 0.0013
What is the probability P(99.3 < X ≤ 100.5)?
 

As above but make the screen read

    normalcdf
lower:99.3
upper:100.5
μ:100
σ:15/√(900)    
Paste

Answer:  0.7605880293, round to 0.7606

Edwin
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