Pia's marks in Year 10 assessments are shown. The scores for each subject were normally distributed.
In which subject did Pia perform best in comparison with the rest of Year 10?
- English
- Mathematics
- Science
- History
Statistics, 2ADV S3 2021 HSC 32
In a particular city, the heights of adult females and the heights of adult males are each normally distributed.
Information relating to two females from that city is given in Table 1.
The means and standard deviations of adult females and males, in centimetres, are given in Table 2.
A selected male is taller than 84% of the population of adult males in this city.
By first labelling the normal distribution curve below with the heights of the two females given in Table 1, calculate the height of the selected male, in centimetres, correct to two decimal places. (4 marks)
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♦ Mean mark 41%.
Statistics, 2ADV S3 2020 HSC 28
In a particular country, the hourly rate of pay for adults who work is normally distributed with a mean of $25 and a standard deviation of $5.
- Two adults who both work are chosen at random.
Find the probability that at least one of them earns between $15 and $30 per hour. (3 marks)
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- The number of adults who work is equal to three times the number of adults who do not work.
One adult is chosen at random.
Find the probability that the chosen adult works and earn more than $25 per hour. (2 marks)
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♦ Mean mark part (a) 40%.
b.
Statistics, 2ADV S3 2020 HSC 3 MC
John recently did a class test in each of three subjects. The class scores on each test were normally distributed.
The table shows the subjects and John's scores as well as the mean and standard deviation of the class scores on each test.
Relative to the rest of class, which row of the table below shows John's strongest subject and his weakest subject?
Statistics, STD2 S5 2018 HSC 27e
Joanna sits a Physics test and a Biology test.
- Joanna’s mark in the Physics test is 70. The mean mark for this test is 58 and the standard deviation is 8.
Calculate the
-score for Joanna’s mark in this test. (1 mark)
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- In the Biology test, the mean mark is 64 and the standard deviation is 10.
Joanna’s
-score is the same in both the Physics test and the Biology test.
What is her mark in the Biology test? (2 marks)
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Statistics, STD2 S5 2017 HSC 29d
All the students in a class of 30 did a test.
The marks, out of 10, are shown in the dot plot.
- Find the median test mark. (1 mark)
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- The mean test mark is 5.4. The standard deviation of the test marks is 4.22.
Using the dot plot, calculate the percentage of the marks which lie within one standard deviation of the mean. (2 marks)
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- A student states that for any data set, 68% of the scores should lie within one standard deviation of the mean. With reference to the dot plot, explain why the student’s statement is NOT relevant in this context. (1 mark)
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Statistics, STD2 S5 2015 HSC 28b
The results of two tests are normally distributed. The mean and standard deviation for each test are displayed in the table.
Kristoff scored 74 in Mathematics and 80 in English. He claims that he has performed better in English.
Is Kristoff correct? Justify your answer using appropriate calculations. (2 marks)
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Statistics, STD2 S5 2007 HSC 25d
The results of two class tests are normally distributed. The means and standard deviations of the tests are displayed in the table.
- Stuart scored 63 in Test 1 and 62 in Test 2. He thinks that he has performed better in Test 1. Do you agree? Justify your answer using appropriate calculations. (2 marks)
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- If 150 students sat for Test 2, how many students would you expect to have scored less than 64? (2 marks)
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i.
ii.
Statistics, STD2 S5 2011 HSC 27c
Two brands of light bulbs are being compared. For each brand, the life of the light bulbs is normally distributed.
- One of the Brand B light bulbs has a life of 400 hours.
What is the
-score of the life of this light bulb? (1 mark)
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- A light bulb is considered defective if it lasts less than 400 hours. The following claim is made:
‘Brand A light bulbs are more likely to be defective than Brand B light bulbs.’
Is this claim correct? Justify your answer, with reference to
-scores or standard deviations or the normal distribution. (2 marks)
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Statistics, STD2 S5 2013 HSC 29b
Ali’s class sits two Geography tests. The results of her class on the first Geography test are shown.
The mean was 68.5 for the first test.
- Calculate the standard deviation for the first test. Give your answer correct to one decimal place. (1 mark)
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- On the second Geography test, the mean for the class was 74.4 and the standard deviation was 12.4.
Ali scored 62 on the first test. Calculate the mark that she needed to obtain in the second test to ensure that her performance relative to the class was maintained. (3 marks)
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