QCEVault

Statistical inference — Question 285

Original QCE Vault practice · 6 marks

Q285 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 285 (6 marks)

Let Φ\Phi be the standard normal cumulative distribution function. A normal population X has unknown mean μ\mu and standard deviation σ>0\sigma>0. It is known that P(X<44)=Φ(1)P(X<44)=\Phi(1) and P(X<36)=Φ(−1)P(X<36)=\Phi(-1).
a)
Determine μ\mu and σ\sigma.
[3 marks]
b)
A sample mean from n independent observations satisfies P(X‾<41)=Φ(1)P(\overline X<41)=\Phi(1). Determine n and explain why its distribution is exactly normal.
[3 marks]
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