Standard Normal Distribution (Edexcel A-Level Mathematics): Quizzes

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Standard Normal Distribution
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What does the inverse normal distribution function provide?

Boundary for a given probability

For calculator use, what does 'area' refer to in inverse normal calculations?

Area to the left of a boundary

If P(X>b)=0.42P(X > b) = 0.42, what area should be entered into the inverse normal calculator?

0.580.58

What is a z-value in a normal distribution?

Number of standard deviations from mean

What is the formula for calculating a z-value?

z=X−μσz = \frac{X - \mu}{\sigma}

For X∼N(27,40)X \sim N(27, 40) where X=18X = 18, what is the z-value?

−1.423-1.423

Why does the median equal the mean in a normal distribution?

The distribution is symmetrical about mean

How is a 10% to 90% interpercentile range calculated?

Subtract 10th percentile from 90th

Why do P(X>38)P(X > 38), P(Y≥26)P(Y \geq 26), P(Z≥2)P(Z \geq 2) all equal 0.02280.0228?

All boundaries are 2 SD from mean

To find unknown μ\mu given a probability, what method is used?

Solve algebraic and numerical z equations

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