Using the Normal Distribution (HSC SSCE Mathematics Advanced): Quizzes

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Using the Normal distribution
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According to the empirical rule, what % of values fall within 1 standard deviation of the mean?

68%

What % of values in a normal distribution fall within 3 standard deviations of the mean?

99.7%

If mean is 102, SD is 2, what is the z-score for a value of 100?

−1-1

What does a negative z-score indicate about a value?

Falls below the mean

If 68% of values fall between Z=−1Z=-1 and Z=1Z=1, what % falls outside this range?

32%

If 32% falls outside Z=−1Z=-1 to Z=1Z=1, what % falls below Z=−1Z=-1 by symmetry?

16%

What do standard normal probability tables show?

Cumulative probabilities below z-scores

If table shows P(Z≤1.5)=93%P(Z \leq 1.5) = 93\%, what is P(Z>1.5)P(Z > 1.5)?

7%

Bars: mean 102g, SD 2g. What % weigh more than 105g if P(Z≤1.5)=93%P(Z \leq 1.5) = 93\%?

7%

For P(Z≤−3.1)=0.001P(Z \leq -3.1) = 0.001, what mean gives P(weight<100)=0.001P(\text{weight} < 100) = 0.001 if SD is 2g?

106.2g

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