Finding X in Normal Distributions
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Objective
I can determine the value of x corresponding to a given probability in a normal distribution.
Part 1 of 4
Warm-up video
Math and Stats Help · 8:42
We don't generate video — this one is by Math and Stats Help on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
To find the x value (random variable) for a normal distribution, you can use the formula: x = mean + (z-score × standard deviation).
- 2
If you are looking for the top tenth percentile, you need to find the z-score that corresponds to an area of 0.9 to the left in the normal table.
- 3
When finding the heights equidistant from the mean that contain 88% of the population, you need to find the z-scores that correspond to 0.06 in each tail (above and below the mean).
Part 3 of 4
Practice
8 questions
What formula is used to find the x value (random variable) in a normal distribution, given the mean, z-score, and standard deviation?
In a normal distribution of women's heights, the mean is 64 inches and the standard deviation is 3 inches. If a woman is in the top 5th percentile, would you expect her height to be above or below 64 inches? Explain.
Part 4 of 4
Exit ticket
Quick comprehension check
“The heights of men are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. Find the height corresponding to the 90th percentile. Show your work, including the z-score you used.”
Sample answer included in the free materials
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