SOLUTION: For a standard normal distribution, find: P(-2.24 < z < 0.12)

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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
  1. Press the button labeled "2nd"
  2. Press the VARS key
  3. 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.
  4. 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
  5. 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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