The histogram shows a summary of scores on a test.
Provide TWO features of the histogram that indicate that the data comes from a normal distribution. (2 marks)
Statistics, STD2 S5 2022 HSC 13 MC
A random variable is normally distributed with mean 0 and standard deviation 1 . The table gives the probability that this random variable lies below
The probability values given in the table are represented by the shaded area in the following diagram.
What is the probability that a normally distributed random variable with mean 0 and standard deviation 1 lies between 0 and 1.94 ?
- 0.0262
- 0.4738
- 0.5262
- 0.9738
Statistics, STD2 S5 2021 HSC 41
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 16%.
Statistics, STD2 S5 2019 HSC 15 MC
The scores on an examination are normally distributed with a mean of 70 and a standard deviation of 6. Michael received a score on the examination between the lower quartile and the upper quartile of the scores.
Which shaded region most accurately represents where Michael's score lies?
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Statistics, STD2 S5 2004 HSC 24c
The normal distribution shown has a mean of 170 and a standard deviation of 10.
- Roberto has a raw score in the shaded region. What could his
-score be? (1 mark)
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- What percentage of the data lies in the shaded region? (2 marks)
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Statistics, STD2 S1 2006 HSC 8 MC
Which of these graphs best represents positively skewed data with the smaller standard deviation?
Statistics, STD2 S5 2008 HSC 28a
The following graph indicates
- What is the
-score for a six year old girl of height 120 cm? (1 mark)
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- Rachel is 10 ½ years of age.
(1) If 2.5% of girls of the same age are taller than Rachel, how tall is she? (1 mark)
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(2) Rachel does not grow any taller. At age 15 ½, what percentage of girls of the same age will be taller than Rachel? (2 marks)
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- What is the average height of an 18 year old girl? (1 mark)
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For adults (18 years and older), the Body Mass Index is given by
The medically accepted healthy range for
- What is the minimum weight for an 18 year old girl of average height to be considered healthy? (2 marks)
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- The average height,
, in centimetres, of a girl between the ages of 6 years and 11 years can be represented by a line with equation
where is the age in years.
(1) For this line, the gradient is 6. What does this indicate about the heights of girls aged 6 to 11? (1 mark)
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(2) Give ONE reason why this equation is not suitable for predicting heights of girls older than 12. (1 mark)
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Statistics, STD2 S5 2010 HSC 4 MC
Which of the following frequency histograms shows data that could be normally distributed?
