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Statistics, STD2 EQ-Bank 35

The life span of light globes from a particular factory is normally distributed with a mean of 840 hours and a standard deviation of 80 hours.

Light globes which have a life span between 600 hours and 712 hours are considered to have a short life span.

Light globes which have a life span between 1000 hours and 1112 hours are considered to have a long life span.

Explain, with reference to areas under the normal distribution curve, whether the number of light globes with a short life span is expected to be more or less than the number of light globes with a long life span.   (3 marks)
 

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\(\text{Sketch the normal curve:}\ \mu=840, \ \sigma=80\)

 

\(\text{Since the area shown for the “short life span” is closer to the mean,}\)

\(\text{it is a larger area. It can therefore be expected that there are more}\)

\(\text{light globes with a short life span than with a long life span.}\)

Show Worked Solution

\(\text{Sketch the normal curve:}\ \mu=840, \ \sigma=80\)

 

\(\text{Since the area shown for the “short life span” is closer to the mean,}\)

\(\text{it is a larger area. It can therefore be expected that there are more}\)

\(\text{light globes with a short life span than with a long life span.}\)

Statistics, STD2 S5 2023 HSC 18

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)

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`text{Choose two from the following features:}`

    • `text{Data distribution is symmetrical about the mean}`
    • `text{Mean = median = mode}`
    • `text{Histogram has only a single peak}`
Show Worked Solution

`text{Choose two from the following features:}`

    • `text{Data distribution is symmetrical about the mean}`
    • `text{Mean = median = mode}`
    • `text{Histogram has only a single peak}`
♦♦ Mean mark 31%.

Statistics, 2ADV S3 2020 HSC 9 MC

Suppose the weight of melons is normally distributed with a mean of `mu` and a standard deviation of `sigma`.

A melon has a weight below the lower quartile of the distribution but NOT in the bottom 10% of the distribution.

Which of the following most accurately represents the region in which the weight of this melon lies?
 

A. B.
C. D.
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`C`

Show Worked Solution

`text(Distributions using)\ mu and sigma:`
 

 
`text(Adjusting the above to identify the interval  10% < weight < 25%)`

  
`=>C`

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?
 

A.
 		 B.
 
C. D.
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`A`

Show Worked Solution

`text{68% of marks lie between 64 and 76 (mean ± 1 σ).}`

♦♦♦ Mean mark 17%.

`text(50% of marks lie between)\ Q_1\ text(and)\ Q_3.`

`=> A`

Statistics, STD2 S5 2004 HSC 24c

The normal distribution shown has a mean of 170 and a standard deviation of 10.
 

  1. Roberto has a raw score in the shaded region. What could his `z`-score be?   (1 mark)

  2. What percentage of the data lies in the shaded region?   (2 marks)

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a.    `1 <= text(z-score) <= 2`

b.    `text(13.5%)`

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a.    `ztext{-score(180)}= (x-mu)/sigma= (180-170)/10= 1`

`ztext{-score(190)}= (190-170)/10= 2`

 `:. 1 <= ztext(-score) <= 2`

 

b.    

`text(From the graph above:)`

`text(13.5% lies in the shaded area.)`

Statistics, STD2 S5 2010 HSC 4 MC

Which of the following frequency histograms shows data that could be normally distributed?
 

Capture1

Capture2 

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`A`

Show Worked Solution

`text(Normally distributed data have a frequency)`

`text(histogram graph that is shaped like a bell.)`

`=>  A`