QCEVault

Statistical inference — Question 244

Original QCE Vault practice · 6 marks

Q244 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 244 (6 marks)

Independent X equals 10 with probability 0.1, and 0 otherwise. For n=100, let K count the observations equal to 10. Then K∼Bin⁡(100,0.1)K\sim\operatorname{Bin}(100,0.1) and X‾=K/10\overline X=K/10.
a)
Determine population mean and standard deviation.
[2 marks]
b)
Find P(X‾≥1.5)P(\overline X\ge1.5) from the exact binomial model.
[2 marks]
c)
Approximate the same probability using the CLT without continuity correction, and explain the difference.
[2 marks]
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