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Statistical inference — Question 13

QCAA 2020, Paper 2 · 6 marks

Q13 · 2020 · Technology-activeSimple familiar6 marks

QUESTION 13 (6 marks)

Data records show that the speeds of cars at a particular location on a highway are normally distributed with a mean of 98.7 km h−1^{-1} and a standard deviation of 4.1 km h−1^{-1}. The speed limit at this location is 100 km h−1^{-1}. A police officer plans to randomly select a sample of 20 cars.
a)
Determine the expected number of cars in the sample that will be travelling within ±1\pm1 km h−1^{-1} of the population mean.
[2 marks]
b)
Determine the probability that the mean speed of this sample will exceed the speed limit.
[2 marks]
c)
There is a 5% probability that the mean speed of this sample will exceed kk km h−1^{-1}. Determine the value of kk.
[2 marks]
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