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Consider a population with 3 observations: 6, 10 and 12. You use simple random sampling without replacement to select a sample of 2 observations. What is the probability that the sample mean is larger than 8?

User Willam
by
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1 Answer

5 votes

Answer:


(2)/(3)

Explanation:

Given that:

The number of observations is:

6, 10, 12

If we are to use a simple random sampling without replacement, then we will have:

(6,10) (6,12) (10,12)

Here;

the sample size n = 2

The population size N = 3

For (6,10) ; The sample mean =
(6+10)/(2)

=
(16)/(2)

= 8

For (6,12) ; The sample mean =
(6+12)/(2)

=
(18)/(2)

= 9

For (10, 12) ; The sample mean =
(10+12)/(2)

=
(22)/(2)

= 11

The probability distribution of sample mean(x) is:

X 8 9 11

P(X=x)
(1)/(3)
(1)/(3)
(1)/(3)

Thus, the probability that the sample mean is larger than 8 is:

P(X> 8) = P(X = 9) + P(X + 11)

P(X> 8) =
(1)/(3)+(1)/(3)

P(X > 8) =
(1+1)/(3)

P(X> 8) =
(2)/(3)

User Selecsosi
by
7.9k points

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