Practice Worked Examples (7) - Normal Distribution - IB 10 Mathematics

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6 sample questions

Question 1.
What is the Z-score for X = 54 when X ~ N(50, 8)?
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Use Z = (X - μ) / σ.
Question 2.
If P(Z < 1) is 0.8413, what is P(Z < -1)?
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Look at the symmetry of the distribution.
3Question 3.
What is the Z-score when X = 60, μ = 50, and σ = 10?
- 1
- 0.5
- 2
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Remember the Z-score formula.
4Question 4.
True or False: In a normal distribution, mean, median, and mode are equal.
- True
- False
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Think about the symmetry of the distribution.
Question 5.
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?
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Use Z = (X - μ) / σ to convert.
Question 6.
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%?
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Use the standard Z-table for the 98th percentile.

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