SOLUTION: Find the indicated probability given that Z is a random variable with a standard normal distribution. (Round your answer to four decimal places.)
P(0 ≤ Z ≤ 1.23)
P(0 ≤ Z â‰
Algebra ->
Probability-and-statistics
-> SOLUTION: Find the indicated probability given that Z is a random variable with a standard normal distribution. (Round your answer to four decimal places.)
P(0 ≤ Z ≤ 1.23)
P(0 ≤ Z â‰
Log On
Question 1204309: Find the indicated probability given that Z is a random variable with a standard normal distribution. (Round your answer to four decimal places.)
P(0 ≤ Z ≤ 1.23)
P(0 ≤ Z ≤ 1.23) = Found 2 solutions by MathLover1, math_tutor2020:Answer by MathLover1(20849) (Show Source):
Method 1 is to use a Z table such as this https://www.ztable.net/
to find that
P(Z < 0.00) = 0.5
P(Z < 1.23) = 0.89065
So,
P(a < Z < b) = P(Z < b) - P(Z < a)
P(0 < Z < 1.23) = P(Z < 1.23) - P(Z < 0)
P(0 < Z < 1.23) = 0.89065 - 0.5
P(0 < Z < 1.23) = 0.39065
P(0 < Z < 1.23) = 0.3907
Method 2 involves a calculator such as this one https://davidmlane.com/normal.html
The mean and standard deviation are 0 and 1 respectively.
Click the "between" and fill in the values 0 and 1.23 to have 0.3907 show up.
Another calculator you can use is a TI83 or TI84.
Refer to this article. https://www.statology.org/normal-probabilities-ti-84-calculator/
Use the normalCDF function to get the area under the curve.
The input that you'll type in is: normalCDF(0,1.23)
Or optionally you could type in normalCDF(0,1.23,0,1)
The TI84 should display the approximate result 0.3906513828 which rounds to 0.3907
Yet another method is WolframAlpha
Type in P(0 < z < 1.23) and you should get roughly 0.390651 which rounds to the answer shown above.
Caution: WolframAlpha is a great resource, but it has a glaring flaw. The graph shown on the page is not correct. The normal distribution curve should be entirely above the x axis. I don't know why some parts of it are below the x axis. I would hope the people running that website would fix the error soon. Rely on the diagram produced by the davidmlane website.
As you can see, there are a lot of ways to calculate the normal distribution probabilities.
Feel free to explore other options.
(
