M=76, SD=19, N=45; what score is represents 2 SDs above the mean.

Question

M=76, SD=19, N=45; what score is represents 2 SDs above the mean? What score represents 2 SD's below the mean? What z-score represents a probability of 0.005? what is the exam score associated with the z-score?

Answer 1

If the standard deviation is 19, then it follows that two standard deviations are 19x2=38.

If the mean, aka average, is 76, then two standard deviations above the mean would be 76+38=114, and two below would be 76-38=38.

The z-score is an expression of a value compared to the mean. In a standard distribution bell curve, a z-score of 0 would be the center line. The z-score allows for comparing different samples to one another. The formula to calculate z-scores is the score minus the mean divided by the standard deviation.

Applying probability to research means you estimate where in the distribution your value falls. An interval estimate provides a range within which the value is expected to fall. A confidence interval is an interval estimate of a population parameter, in other words, the sample mean is an approximation of the population mean, but we want to know how good an approx it is. I'm not sure about the "0.005" from the question, or whether 76 is the sample or population mean, but a reasonable confidence interval is commonly expressed as 95% (0.05), i.e. if the experiment were repeated 100 times, it would contain the population parameter 95 times. A 95% confidence interval for the z-score means it will fall between -1.96 and +1.96 standard deviations, which is slightly lower than 2x (i.e. 113.24 and 38.76, respectively).

Hope this helps!