A random variable
where
Show that
Statistics, 2ADV S3 2021 HSC 33
People are given a maximum of six hours to complete a puzzle. The time spent on the puzzle, in hours, can be modelled using the continuous random variable
The graph of the probability density function is shown below. The graph has a local maximum.
- Show that
. (2 marks)
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- Show that the mode of
is two hours. (2 marks)
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- Show that
. (2 marks)
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- The Intelligence Quotient (IQ) scores of people are normally distributed with a mean of 100 and standard deviation of 15.
- It has been observed that the puzzle is generally completed more quickly by people with a high IQ.
- It is known that 80% of people with an IQ greater than 130 can complete the puzzle in less than two hours.
- A person chosen at random can complete the puzzle in less than two hours.
- What is the probability that this person has an IQ greater than 130? Give your answer correct to three decimal places. (2 marks)
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Statistics, 2ADV S3 EQ-Bank 16
A probability density function is defined by
- Find the value of
. (2 marks)
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- Sketch the probability density function. (1 mark)
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- Find an expression for the cumulative distribution function. (2 marks)
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Show Answers Only
Show Worked Solution
i.
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iii.
COMMENT: Understand why you can check your equation here by confirming
Statistics, 2ADV S3 SM-Bank 10
A continuous random variable,
The median of
Determine the value of
Statistics, 2ADV S3 SM-Bank 5 MC
The function
The value of
A.
B.
C.
D.