Let X N1 4 Find the 75 confidence interval for XSolutionGiv

Let X = N(1, 4). Find the 75% confidence interval for X.

Given X ~ N(1,4)

Here mean = 1 and variance =4

Thus standard deviation= 2

75% CI for X is given by (X\' - Z ?/ sqrt(n) , X\' + Z ?/ sqrt(n) )

Here n is the sample size which is not mentioned in the question.

the Z value corresponding to 75% confidence interval is 0.32

Thus CI is (1-0.32*2/sqrt(n) , 1+0.32*2/sqrt(n))

= ( 1 - 0.64/sqrt(n) , 1+ 0.64/sqrt(n))

Given a certain value of the sample size n, the CI can be found.