QCEVault

Sampling and proportions — Question 311

Original QCE Vault practice · 4 marks

Q311 · Practice questionTechnology-activeSimple familiar4 marks

QUESTION 311 (4 marks)

In a very large population of commuters, 30%30\% use a bicycle at least once a week. A random sample of 200200 independent commuters is selected. Let p^\widehat p be the sample proportion who do so.
Normal approximation for the sample proportion with mean 0.3; the upper tail beyond 0.35 is hatched.
a)
Determine the mean and standard deviation of p^\widehat p.
[2 marks]
b)
Use a normal approximation, without a continuity correction, to estimate P(p^>0.35)P(\widehat p>0.35) to four decimal places.
[2 marks]
Question linkSyllabus coverage

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