SOLUTION: Find the indicated probability assuming that x is a random variable with a normal distribution with the given mean and standard deviation. (Round your answer to four decimal places

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Question 1204317: Find the indicated probability assuming that x is a random variable with a normal distribution with the given mean and standard deviation. (Round your answer to four decimal places.)
P(41 ≤ x ≤ 116), 𝜇 = 10, 𝜎 = 50
0.6715

Incorrect: Your answer is incorrect.
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by math_tutor2020(3816) About Me  (Show Source):
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Answer: 0.2506

Explanation

As one method, you can use a table similar to what is described in this previous question
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1204309.html
But you'll need to convert each raw score to a z score.
Use the formula: z = (x - mu)/sigma

Or you can use a TI83/TI84
https://www.statology.org/normal-probabilities-ti-84-calculator/
The input would be normalCDF(41,116,10,50)
The template in general is normalCDF(lower,upper,mean,standard deviation)

The result of that calculation is approximately 0.2506258718 which rounds to 0.2506

Or you can use this stats calculator that provides a diagram
https://davidmlane.com/normal.html

If you use WolframAlpha, be careful that the diagram shown on WolframAlpha is not correct. The normal distribution curve should be entirely above the x axis. Refer to the first link for a comparison of what I mean.