A data set has a mean of 720 and a standard deviation of 6. Which is closest to the z-score for an element of this data set with a value of 709?

Question

mathmale · Answer

Excuse me: that formula has sigma in the denominator:$$z=\frac{ x-\mu  }{ \sigma }$$

mathmale · Answer

substitute the given value of x, the value of the mean (mu) and the value of the std. dev.  Show your work.  Approx. what value do you obtain for z?

myrandaharris9698 · Answer

so....is it $$z=709-720\div6$$ ?

mathmale · Answer

Not wanting to be overly picky, but still concerned:  You MUST enclose 709-720 inside parentheses.  Otherwise you're on track.

mathmale · Answer

If you don't enclose 709-720 within parentheses, your math statement looks like 709 - 720/6, which is incorrect.

zarkon · Answer

Since this data appears to be from a sample I would use $$z=\frac{x-\overline{x}}{s}$$
as your formula...though it doesn't really change anything numerically.

myrandaharris9698 · Answer

oh okay....so z= (709-720)/6?

mathmale · Answer

Much better.  Please evaluate z now.

myrandaharris9698 · Answer

Would z= - 11/6?

mathmale · Answer

Yes.  that should match one of your answer choices.  Nice work.

myrandaharris9698 · Answer

@Zarkon  what does the x with a line above mean? Is that mean? or deviation?

zarkon · Answer

sample mean

mathmale · Answer

Zarkon:  Mind explaining why this appears to be a sample rather than a population?

myrandaharris9698 · Answer

Thank you both for the help! I really appreciate it. Do you mind to help with a few more?

zarkon · Answer

it is very unusual to have the entire population data.  If it is population data then it should state that.

zarkon · Answer

though...in this case it doesn't matter since the two formulas are numerically the same