### Standard score; performance in a run

Question Sample Titled 'Standard score; performance in a run'

The time used to finish a ${100}$ $\text{m}$ run by a group of university students in two tests is recorded. In the first test, the mean and the standard deviation are ${18}$ $\text{s}$ and ${2}$ $\text{s}$ respectively. In the second test, the mean and the standard deviation are ${16}$ $\text{s}$ and ${1}$ $\text{s}$ respectively. The standard score of George in the first test is ${0.5}$ .

 (a) Find the time that George used to finish the run in the first test. (2 marks) (b) Assume that the time distribution in each of the above tests are normally distributed. George uses ${17}$ $\text{s}$ to finish the race in the second test. He claims that comparing to other students, he performs better in the second test than that in the first test. Is his claim correct? Explain your answer. (2 marks)

 (a) Let ${x}$ $\text{s}$ be the time that George used to finish the run. $\dfrac{{{x}-{18}}}{{2}}$ $={0.5}$ 1M ${x}$ $={19}$ ∴  The time is ${19}$ $\text{s}$ . 1A (b) Standard score $=\dfrac{{{17}-{16}}}{{1}}$ 1M  $={1}$  $>{0.5}$ 1A ∴  George performs worse in the second test comparing to other students. His claim is not correct.

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