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9.055 Empirical rule with z-scores

Interactive practice questions

If Dave scores $96$96 in a test that has a mean score of $128$128 and a standard deviation of $16$16, what is his $z$z-score?

Easy
< 1min

Frank finishes a fun run in $156$156 minutes. If the mean time taken to finish the race is $120$120 minutes and the standard deviation is $12$12 minutes, what is his $z$z-score?

Easy
< 1min

If Iain's $z$z-score in a test is $1$1, the mean mark is $62%$62% and standard deviation is $3%$3%, what is $X$X, his test score?

Easy
< 1min

If Rochelle's $z$z-score in a test is $-3$3, the mean mark is $75%$75% and standard deviation is $3%$3%, find her test score, $X$X.

Easy
< 1min
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Outcomes

4.4.1.4

understand standardised normal variables (z-values, z-scores) and use these to compare samples

4.4.2.2

recognise features of the graph of the probability density function of the normal distribution with mean 𝜇 and standard deviation 𝜎 and the use of the standard normal distribution

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