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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

Work with the stated normal distribution

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

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

Find the probability of 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

Format: empirical-rule estimate