Question

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5. We are given a normal random variable with population mean μ and population standard deviation σ 40.0. (a) How large should a sample size be, in order that, with 96% confidence, the error in estimating μ by the observed sample mean is: (i) at most 10.0? (ii) at most 5.0? (b) Let X denote the (theoretical) sample mean from a random sample of size 25. What is P( X-씨 > 4.0 ) ?

Answer 1

#5.
i) at most 10
Given CI Level = 96%
Margin of Error(ME) = 10
std. dev. = 40.0000
z-value of 96% CI = 2.0537

n = (z*sigma/ME)^2
= (2.0537*40/10)^2
= 67.49
i.e. 68

ii) at most 5
n = (z*sigma/ME)^2
= (2.0537*40/5)^2
= 269.94
i.e. 270