Suppose

x_(1),x_(2),x_(3)

are random sample from

N(\\\\mu ,\\\\sigma ^(2))

distribution. Let

\\\\bar{x} =(1)/(3)\\\\sum_(i=1)^3 x_(i)

.\ Which statement is correct?\ (I)

\\\\bar{x}

has a

N(\\\\mu ,\\\\sigma ^(2))

distribution.\ (II)

\\\\bar{x}

has a

N(\\\\mu ,(\\\\sigma ^(2))/(3))

distribution.\ (III)

\\\\bar{x}

approximately has

N(\\\\mu ,(\\\\sigma ^(2))/(3))

distribution by the CLT.\ (IV) Since

n=3

is not sufficiently large,

\\\\bar{x}

does not have a normal distribution.

Suppose X1,X2,X3 are random sample from N(,2) distribution. Let X=31i=13Xi. Which statement is correct? (I) X has a N(,2) distribution. (II) X has a N(,32) distribution. (III) X approximately has N(,32) distribution by the CLT. (IV) Since n=3 is not sufficiently large, X does not have a normal distribution