Question

Suppose that x is a Normally distributed random variable with an unknown mean μ and known standard deviation 6. If we take repeated samplesof size 100 and compute the sample means x , 95% of all of these values of x should lie within a distance of _____ from μ . (Use the 68‑95‑99.7 rule.)

Answer 1

1.2

Explanation:

Given that X is Normally distributed random variable with an unknown mean μ and known standard deviation 6

Hence we can say for a sample of size 100, the sample mean will have a std deviation of =
`(6)/(√(100) ) =0.6`

Since population std deviation is known we can use Z critical value for finding out the confidence interval

For 95% using (68-95-99.7 rules) we have z critical value =2

Hence margin of error =2(std error) = 1.2

Confidence interval 95%

Lower bound = Mean - margin of error = Mean -1.2

UPper bound = Mean +1.2

Hence , 95% of all of these values of x should lie within a distance of __1.2___ from μ .