Question 1200287: For a standard normal distribution, find:
P(-2.24 < z < 0.12)
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer: 0.5352 (approximate)
Explanation:
If you have a TI83 or TI84 calculator, then follow these steps- Press the button labeled "2nd"
- Press the VARS key
- Scroll down to normalcdf. The template is normalcdf(L, U, mu, sigma) where L, U are the lower and upper boundaries. The mu and sigma are the mean and standard deviation.
- Type in normalcdf(-2.24, 0.12, 0, 1) or you could optionally type in normalcdf(-2.24, 0.12) and the calculator will assume the default mu and sigma values of 0 and 1 respectively which applies to the standard normal Z distribution
- Whichever route you take for the previous step, the calculator should produce a value of roughly 0.5352130507. Round that to four decimal places to get 0.5352
Here is another useful calculator
https://davidmlane.com/normal.html
It also provides a diagram of the shaded area under the normal curve.
If you want to use a table such as this one (or similar found in the back of your book), then follow these steps:
P(z < -2.24) = 0.01255
P(z < 0.12) = 0.54776
P(a < z < b) = P(z < b) - P(z < a)
P(-2.24 < z < 0.12) = P(z < 0.12) - P(z < -2.24)
P(-2.24 < z < 0.12) = 0.54776 - 0.01255
P(-2.24 < z < 0.12) = 0.53521
P(-2.24 < z < 0.12) = 0.5352
In the link I posted, scroll down to the section labeled "How to Read The Z Table" for an example.
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