Xn are independent random variables and each one of them has a normal distribution with mean...

Xn are independent random variables and each one of them has a normal distribution with mean 0 and variance 1

what is the distribution of X-bar if n=9

what is the probability of X-bar =<3 if n=9

Solutions

Expert Solution

Solution :

Given that ,

mean = = 0

standard deviation = = 1

n = 9

= 0 and = 1

² = 1

= / n = 1 / 9 = 1 / 3

(a)

~ N( , )

~ N(0 , 1/3 )

(b)

P( 3) = P(( - ) / < (3 - 0) / 1/3)

= P(z < 9)

Using standard normal table,

Probability = 0

milcah answered 9 months ago

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