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If you used the sample values you should get z scores of ≲,2. Choose either one of them.Ĭalculate Z2 in the same way. )/σ or using the excel function STANDARDIZE(x, mean, S.D). There are two ways to do this, either using the formula we learned in class (X- m Below Z1 we will calculate the standard score of X1. These values are usually given to you in questions. Questions about the normal distribution often ask you to calculate the area under the curve between two scores or the probability that a score would turn out to be between two scores. Try other values of p, m and S.D in order to get a better feeling for the use of this function. This means that 84.135% of the population have a score below 102 in a population with that is normally distributed with a mean of 100 and S.D of 2. (if you used the sample values, you should get a score close to 102 which was the x value from #3. Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.Ĥ) a) Type into different cells a probability,mean and S.D (for example p = 0.84134, m =100, s.d = 2), don’t forget to add a label so you’ll know what you put in this cell.ī) In a cell next to it, enter the function NORMINV(probability,mean,s.d), use the addresses of the cells where you placed the probability, mean and S.D. NORMINV( probability, mean, standard_dev) Try other values of x, m and s.d in order to get a better feeling for the use of this function. (if you used the sample values, you should get an area of 0.8413. You can also enter the word TRUE into a cell so you can use it in the function.ī) In another cell enter the function NORMDIST(x,mean,SD,cumulative), use the address of the cells where you placed the x,mean,sd,TRUE. Don’t forget to add a label so you’ll know what you put in this cell, for example use, x=102,m=100,sd = 2.

IN THIS EXERCISE USE "TRUE" SINCE YOU WANT THE AREA UNDER THE CURVE.ģ) a) Enter your score, mean, S.D to different cell in Excel. If cumulative is TRUE, NORMDIST returns the cumulative distribution function if FALSE, it returns the probability mass function. Standard_dev is the standard deviation of the distribution.Ĭumulative is a logical value that determines the form of the function. Mean is the arithmetic mean of the distribution. X is the value for which you want the distribution. NORMDIST( x, mean, standard_dev, cumulative) Excel has several functions that will let you compute areas under the curve directly from your scores without standardizing them first. In real life, we usually deal with normal distributions that are not standardized, so they are not expressed in z scores. What would you get if you used a p = 0.97724 (you should get a value close to 2, your z from #1) Try other values of p in order to get a better feeling for the use of this function, for example 0.5,0.99. (if you used p=0.975, you should get a z score of 1.95996. a) Pick a cell and enter a probability into it (for example 0.975), don’t forget to add a label so you’ll know what you put in this cell.ī) In a cell next to it, enter the function NORMSINV(probability), use the address of the cell where you placed the probability.

NORMSINV will return a z score that corresponds to an area under the curve. The distribution has a mean of zero and a standard deviation of one. Returns the inverse of the standard normal cumulative distribution. Probability is a probability corresponding to the normal distribution. Try other values of z in order to get a better feeling for the use of this function, for example 0,1,5,-1,-3) (if you used z=2, you should get an area of 0.97724 or in other words, more than 97% of the population have scores lower then your z.