SOLUTION: Let z be a standard normal random variable with mean 𝜇 = 0 and standard deviation 𝜎 = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal
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Question 1206850: Let z be a standard normal random variable with mean 𝜇 = 0 and standard deviation 𝜎 = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal places.)
P(z > 1.13) =
As the instructions mention, turn to the page that has Table 3 in Appendix I.
Locate the row that starts with 1.1
Locate the column that has 0.03 at the top.
The intersection of this row and column yields the approximate value 0.87076
It indicates that P(Z < 1.13) = 0.87076 approximately.
For students following along that don't have their stats textbook with them, refer to online resources such as this https://www.ztable.net/
Then,
P(Z > 1.13) = 1-P(Z < 1.13)
P(Z > 1.13) = 1-0.87076
P(Z > 1.13) = 0.12924
P(Z > 1.13) = 0.1292 which is the final answer when rounding to 4 decimal places.
There are many ways to verify this with a handheld calculator, an app on your phone, or a website.
Feel free to explore your favorite method.
It's probably best to use a tool that is approved by your teacher for exam settings.
Once you get outside of the classroom, you can of course choose any method you want.
On the TI84 is the command called NormalCDF which is found by pressing the button labeled "2nd" and then pressing the VARS key.
The command to type in would be NormalCDF(1.13,999) where mu = 0 and sigma = 1 are the default options.
The 999 is to represent some really large number effectively acting as "infinity" so to speak.
You can also use an online tool such as this https://davidmlane.com/normal.html
Which is completely free and offers a more intuitive user interface. No need to memorize function commands or what inputs go where.
As a bonus, it offers a really nice diagram as well.
Notice this diagram has the curve entirely above the x axis.
Whereas WolframAlpha has a flaw to it when offering a diagram.
This is what shows up when you type in P(Z > 1.13) and select the "referring to statistics" option.
Some parts of this curve are mistakenly below the x axis. That's not good.
I'm not sure why WolframAlpha has this weird flaw. But it's something to keep in mind.
Tutor @MathLover1 appears to have used this slightly faulty diagram.
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