Practice Finding Probabilities (5) - Normal Distribution - IB 10 Mathematics

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10 questions

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4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the formula for calculating tail probability?
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Think about the complement of the probability.
Question 2.
Define what a Z-score is.
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Consider how standard deviations relate to the average.
3Question 3.
What is the formula to calculate the tail probability?
- P(X > x) = P(X ≤ x)
- P(X < x) = 1 - P(X > x)
- P(X > x) = 1 - P(X ≤ x)
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Consider the definition of tail probabilities.
4Question 4.
True or False: The Z-score for a data point that is exactly at the mean is 0.
- True
- False
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Think about how the Z-score is calculated.
Question 5.
Given a dataset with $mean = 200$ and $sd = 25$ , calculate $P(250 < X < 300)$ and interpret your results.
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Remember to use the standardization formula for both bounds.
Question 6.
If the 95th percentile of a distribution is 130 with mean 100, what is the new mean if the distribution shifts right by 40?
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Consider how shifts affect entire distributions, not just individual percentiles.

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