TopicName Test - Jacaranda
WorkSHEET 10.1 Statistics Name: ___________________________
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| |In a class test where the mean was 62% and the standard deviation |[pic] |5 |
| |12.6%, Jan received 74%. Calculate her result as a z-score. | | |
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| |On the same test, Bob received 50%. What is Bob’s result as a z-score?|[pic] |5 |
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| |The heights of eight professional basketball players are (in |Enter the data into a calculator which provides statistical |6 |
| |centimetres): |calculations. | |
| |188, 189, 192, 193, 194, 194, 195, 195. |[pic] | |
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| |Calculate the mean and standard deviation of their heights (to |[pic] | |
| |one decimal place). | | |
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| |John is 190 cm tall. Express his height as a z-score compared with the| | |
| |basketball players’ heights (to one decimal place). | | |
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| |Bill’s height, when converted to a z-score compared with the |Bill’s height is one standard deviation above the mean height of the |4 |
| |basketball players in question 3, is +1. What is Bill’s height? |basketball players. | |
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| | |So, Bill’s height = 192.5 cm + 2.5 cm | |
| | |= 195 cm | |
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| |Ryan received 82% in his History exam where the mean was 70% and the |[pic] [pic] |5 |
| |standard deviation 10%. In his Biology exam he received 75% when the | | |
| |mean was 50% and the standard deviation 12%. He felt he had performed |Ryan is 1.2 standard deviations above the class mean in History and | |
| |better in History than in Biology. Is this the case? Explain. |2.1 standard deviations above the class mean in Biology. He has | |
| | |therefore performed better in Biology than History. | |
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| |In international swimming the mean time for the men's 100 m freestyle |[pic] [pic] |5 |
| |is 50.46 sec with a standard deviation of 0.6 sec. For the 200 m | | |
| |freestyle, the mean time is 110.4 sec with a standard deviation of 1.4|Jason’s z-score for the 100 m is lower, indicating that his time is | |
| |sec. |further below the mean for this event than for the 200 m event. So, he| |
| | |should enter the 100 m event. | |
| |Jason’s best time for the 100 m is 48.76 sec and for the 200 m is | | |
| |108.43 sec. | | |
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| |If he can only enter one of these events in the competition, which one| | |
| |should he enter? | | |
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| |What percentage of the scores lie: |68% of the scores lie within one standard deviation either side of the|6 |
| |within one standard deviation of the mean? |mean. | |
| |within two standard deviations of the mean? |95% of the scores lie within two standard deviations either side of | |
| |within three standard deviations of the mean? |the mean. | |
| | |99.7% of the scores lie within three standard deviations either side | |
| | |of the mean. | |
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| |On a common IQ test, the distribution is normal with a mean of 100 and|[pic] [pic] |5 |
| |a standard deviation of 12. What percentage of the scores lie between | | |
| |76 and 124? |The score of 76 is two standard deviations below the mean and the | |
| | |score of 124 is two standard deviations above the mean. So, 95% of the| |
| | |scores lie in the range 76 to 124. | |
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| |In the above IQ test in question 8, what range of scores would account|99.7% of the scores lie within three standard deviations either side |4 |
| |for 99.7% of the people? |of the mean. | |
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| | |[pic] | |
| | |So a score 36 below 100 to a score 36 above 100 would account for | |
| | |99.7% of the people. | |
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| | |So the range 64 to 136 would include 99.7% of people. | |
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| |On an end of semester maths test the mean result was 62% and the | [pic] |5 |
| |standard deviation was 12%. | | |
| |What percentage of the results would lie above 86%? |So a score of 86% lies two standard deviations above the mean. 95% of | |
| | |the scores lie within two standard deviations either side of the mean.| |
| | |This means that 5% of the scores lie outside this range. Half of these| |
| | |scores lie below –2 and half above +2. | |
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| | |[pic] Percentage of results above 86% = 2.5% | |
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