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# Normal distrinution question help watch

1. It is given that X-N(50.0,8^2). The mean of 20 random observations of
x is denoted by x̄. Find p( x̄>47).

The part I was stuck on was when you approximate it to the normal distribution 47-50/√8^2-20 is used. I was confused on why √8^2-20 is used. Thanks in advance.
2. (Original post by Butterflyshy)
It is given that X-N(50.0,8^2). The mean of 20 random observations of
x is denoted by x̄. Find p( x̄>47).

The part I was stuck on was when you approximate it to the normal distribution 47-50/√8^2-20 is used. I was confused on why √8^2-20 is used. Thanks in advance.
This looks incorrect - there should be no minus 20.

The distribution of the sample mean would be

Is it perhaps a division, misprinted?
3. (Original post by ghostwalker)
This looks incorrect - there should be no minus 20.

The distribution of the sample mean would be

Is it perhaps a division, misprinted?
It is a division, sorry.
4. (Original post by Butterflyshy)
It is a division, sorry.
I presume you're OK with it now then. If not, what bit don't you follow.
5. (Original post by ghostwalker)
I presme you're OK with it now then. If not, what bit don't you follow.
I don't understand why you use √8^2/20
6. (Original post by Butterflyshy)
I don't understand why you use √8^2/20
The question asks you to find the probability that the sample mean is > 47. For that you need the distribution of the sample mean, which for a r.v. distrubuted is , where n is the sample size.

The standard deviation is then
7. (Original post by ghostwalker)
The question asks you to find the probability that the sample mean is > 47. For that you need the distribution of the sample mean, which for a r.v. distrubuted is , where n is the sample size.

The standard deviation is then
That makes sense

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