Let Xbar be the mean of a random sample of Size 5 from a normal distribution with μ = 0 and σ^2 = 125. Determine c so that Pr(Xbar < c)=0.90.
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Solution. As we know that Xbar will follows a normal distribution with mean mu=0 and the standard deviation sigma/sqrt(n)=sqrt(125)/sqrt(5)=5 (Note: sigma^2=125 and n=5 in this question.),
Note that Z=(Xbar-0)/5~N(0,1). We have
So, the value of c is 6.41.