Practice - Worked Examples
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Practice Questions
Test your understanding with targeted questions
What is the Z-score for X = 54 when X ~ N(50, 8)?
💡 Hint: Use Z = (X - μ) / σ.
If P(Z < 1) is 0.8413, what is P(Z < -1)?
💡 Hint: Look at the symmetry of the distribution.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Z-score when X = 60, μ = 50, and σ = 10?
💡 Hint: Remember the Z-score formula.
True or False: In a normal distribution, mean, median, and mode are equal.
💡 Hint: Think about the symmetry of the distribution.
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Challenge Problems
Push your limits with advanced challenges
A factory produces part sizes that are normally distributed with a mean of 50mm and a standard deviation of 5mm. What is the probability that a part will be between 47mm and 53mm?
💡 Hint: Use Z = (X - μ) / σ to convert.
If test scores are normally distributed with a mean of 75 and a standard deviation of 10, what score would you need to be in the top 2%?
💡 Hint: Use the standard Z-table for the 98th percentile.
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Reference links
Supplementary resources to enhance your learning experience.