Use your calculator to find the areas (percent of data) that satisfy the stated conditions for each normal distribution.  Round each answer to four decimals.  1) Greater than 67, if the mean is...

Use your calculator to find the areas (percent of data) that satisfy the stated conditions for each normal distribution.  Round each answer to four decimals.

1) Greater than 67, if the mean is 60 and the standard deviation is 15

2) Less than 70, if the mean is 63 and the standard deviation is 14

Should I go 2nd than VARS, than 2:normal cdf( ?????

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

(1) Given `mu=60,sigma=15` find `P(x>67)`

First convert 67 to a standard z-score: `z=(67-60)/15=7/15=.4bar(6)`

Then `P(x>67)=P(z>7/15)` . In a TI-83/84 calculator you follow the following steps:

2nd VARS (dist)->2 (normalcdf)

On the homescreen you will see normalcdf(

Input `7/15`

Then ,

Then ``2nd , (EE) 99

Close parantheses and hit enter. The result should be .3203692025

**Alternatively, you can skip converting to a standard z-score. Input normalcdf(67,E99,60,15) and you will get .3203692025 as before. The format is normalcdf`(a,b,mu,sigma)` where a is the lower limit and b the upper limit.

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Thus `P(x>67)~~.3204`

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** This is the area under the standard normal curve from .466666667 to infinity **

(2) Input normalcdf(-E99,70,63,14) and the result should be .6914624678

** Make sure to use the opposite key "-", not the subtract key.**

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`"Then" P(xlt70)~~.6915`

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