Exercises for Question Type 2: Finding the interval for which a specific percentage of data is concentrated

Question 1

Skill question

This question assesses the ability to apply the empirical rule (68-95-99.7 rule) to a normal distribution with a given mean and variance to estimate the percentage of data within a specific interval.

Assuming a normal distribution with mean $μ = 100$ and variance $σ^{2} = 16$ , estimate the percentage of data that lies between 92 and 108.

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Question 2

Skill question

This question assesses the application of the empirical rule (68-95-99.7 rule) for a normal distribution to calculate statistical parameters.

Assuming a normal distribution with mean $μ = 8$ , 95% of data falls between 6.5 and 9.5. Calculate the variance.

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Question 3

Skill question

The distribution is approximately normal with mean $μ = 50$ . This question involves the application of the empirical rule (68-95-99.7 rule) for normal distributions to find the standard deviation and then the variance.

A distribution has mean $μ = 50$ and is approximately normal. If 68% of the data lies between 45 and 55, find the variance.

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IB Mathematics Applications & Interpretation Question Type 2: Finding the Interval for Which a Specific Percentage of Data Is Concentrated Exercises