Question 1199400: Find the area under the SND from 0 to 1.45
Ans: 0.4265
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
You can use an online calculator such as this one
https://davidmlane.com/normal.html
The mean and standard deviation are 0 and 1 respectively.
Click the "between" radio button. Then type in 0 and 1.45 into the left and right boxes in that order.
Then click "recalculate" to have 0.4265 show up.
The normal distribution diagram updates as well.
Yet another calculator is wolfram alpha
Type "normalcdf(0,1.45)" without quotes into the service, and it will display the answer mentioned.
The thing you want is the one that mentions 0 < z < 1.45 (inner).
There are many other similar free online options.
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Or you can use the normalcdf function on your TI83/TI84 calculator.
Press the button labeled "2nd". Then press the "VARS" key.
The normalcdf function is the 2nd item in the list.
The template of the normalcdf function is this
normalcdf(lower,upper,mu,sigma)
where,
lower = left or lower boundary
upper = right or upper boundary
mu = mean
sigma = standard deviation
Another template is
normalcdf(lower,upper)
where the lower and upper are the same as mentioned above.
The other two inputs can be left out, and they are assumed to be 0 and 1 respectively.
These values are used so frequently that it's best to use this shorter template.
In your case you'd type in
normalcdf(0,1.45)
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If your teacher wants you to use a table, then refer to the back of your textbook.
Here is a website that offers a free Z table if you don't have your textbook with you.
https://www.ztable.net/
Use the table to find that
P(z < 0) = 0.5 exactly
P(z < 1.45) = 0.92647 approximately
So,
P(a < z < b) = P(z < b) - P(z < a)
P(0 < z < 1.45) = P(z < 1.45) - P(z < 0)
P(0 < z < 1.45) = 0.92647 - 0.5
P(0 < z < 1.45) = 0.42647
P(0 < z < 1.45) = 0.4265
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