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Calculate probabilities for normal distributions

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
Lower tail: empirical-rule probabilityLower tail: empirical-rule percentageUpper tail: empirical-rule probabilityUpper tail: empirical-rule percentageNOWMix of allRecommended
Question 1 of 8

Calculator allowed

The information for this normal model is given below

Let \(Z\) have distribution \(Z\sim N(0,1)\). The relevant boundary value is \(2\)

Use the region above the boundary

Use the 68–95–99.7% empirical rule to estimate the probability. Use these percentages without intermediate rounding; give the resulting estimate as a fraction or terminating decimal, not a calculator normal-CDF value

(a)1 mark

Select the standard-normal expression for the event

(b)1 mark

Calculate the percentage for the event

Use the 68–95–99.7% empirical rule to estimate the probability. Use these percentages without intermediate rounding; give the resulting estimate as a fraction or terminating decimal, not a calculator normal-CDF value

Express the estimate as a percentage

Format: empirical-rule estimate