Modelling with the normal distribution · Short practice

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Recall

Fitting a normal model — objective 1

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le \frac{75}{2})= \Phi (- \frac{1}{2}), \ P(X\le \frac{213}{5})= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find the standard deviation of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Fitting a normal model — objective 1

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le 38)= \Phi (- \frac{1}{2}), \ P(X\le \frac{224}{5})= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find the standard deviation of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Fitting a normal model — objective 2

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le 38)= \Phi (- \frac{1}{2}), \ P(X\le \frac{224}{5})= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find the mean of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Fitting a normal model — objective 2

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le \frac{77}{2})= \Phi (- \frac{1}{2}), \ P(X\le 47)= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find the mean of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Fitting a normal model — objective 3

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le \frac{77}{2})= \Phi (- \frac{1}{2}), \ P(X\le 47)= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find P(X>40).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Fitting a normal model — objective 3

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le 41)= \Phi (- \frac{1}{2}), \ P(X\le \frac{222}{5})= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find P(X>40).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Fitting a normal model — objective 4

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le 41)= \Phi (- \frac{1}{2}), \ P(X\le \frac{222}{5})= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find the 90th percentile of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Fitting a normal model — objective 4

Maths4U Original · Short practice

A normal X satisfies \(\displaystyle P(X\le \frac{83}{2})= \Phi (- \frac{1}{2}), \ P(X\le \frac{233}{5})= \Phi (\frac{6}{5})\). Here Φ is the standard normal CDF.

Find the 90th percentile of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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