Question

what percent of the total population is found between the mean and the z-score given?

z = 3.37

Answer 1

The mean of a population has a z-score of 0.

Thus the objective here is to find the percentage of the total population between z-scores 0 and 3.37.

Using a normal distribution calculator or an appropriate normal distribution table; the probability that a z-score be less than 3.37 is 0.9996

Also, the probability of a z-score to be less than 0 is 0.5.

Thus, the probability that a z-score is between 0 and 3.37 is the difference between the above two:

i.e. .

Thus 0.4996 portion of the total population is between th mean and z-score of 3.37.

Converting to percentage; .

Therefore 49.96% of the total population is between the mean and the z-score 3.37

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