Unit 4: Statistics and Probability

Topic 4.9: Normal Distribution Questions

Practice 20 exam-style questions for IB Math AI SL Topic 4.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1find2 marks
X ~ N(50, 10²). Find P(X > 65).
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2find2 marks
The contents of cans are N(330, 4²) ml. Find the probability a can has less than 325 ml.
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3find1 mark
Explain why, in AI SL, you do NOT need to convert X to a z-score to find normal probabilities.
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4find1 mark
X ~ N(40, 6²). Write down P(X < 40).
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5find2 marks
Delivery times are N(30, 5²) minutes. Find the probability a delivery takes between 25 and 35 minutes.
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6find2 marks
Heights are N(170, 9²) cm. Find the probability a randomly chosen person is taller than 185 cm.
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7find1 mark
For a normal distribution, state the relationship between the mean, median and mode.
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8find1 mark
State the approximate percentage of data within 1 standard deviation of the mean of a normal distribution.
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9find2 marks
X ~ N(200, 25²). Find P(180 < X < 220).
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10find2 marks
A normal curve has mean 20. State what happens to the curve if the mean increases to 30 (σ unchanged).
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11find1 mark
State the GDC command to find P(X < a) for X ~ N(μ, σ²).
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12find2 marks
X ~ N(50, 10²). Find P(X < 60) using a GDC.
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13find2 marks
X ~ N(70, 8²). Find the value exceeded by the top 15% (i.e. find a with P(X > a) = 0.15).
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14find3 marks
X ~ N(500, 50²). Out of 1000 values, find the expected number greater than 600.
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15find6 marks
The masses of apples are normally distributed with mean 150 g and standard deviation 20 g.
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16find2 marks
Heights are N(165, 8²) cm. Find the percentage of people between 149 cm and 181 cm.
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17find2 marks
X ~ N(70, 8²). Find the value of a such that P(X < a) = 0.90.
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18find2 marks
X ~ N(25, 4²). Find the lower quartile (the value below which 25% of data lies).
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19state5 marks
Two factories produce bolts. Factory A's lengths are N(50, 2²) mm and Factory B's lengths are N(50, 5²) mm.
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20find7 marks
Exam scores are normally distributed with mean 62 and standard deviation 12. Let X be a randomly chosen score.
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