Suppose that people's heights (in centimeters) are normally distributed, with a mean of 175 and a standard deviation of 6. We find the heights of 80 people. How many would you expect to be taller than 170 cm?

Question

directrix · Answer

I think we need the z-score. z = ( 170 - 175)/6 = 5/6 = - .833. That is not quite one standard deviation below the mean.

You will need access to the areas of the standard normal distribution curve and the corresponding z-scores. Before looking for area to z score connection, be sure to look at the top of the table to determine what the areas mean with respect to the mean z-score of 0. Not all tables are arranged the same way.

directrix · Answer

Take a look at this one: http://www.mathsisfun.com/data/standard-normal-distribution-table.html

directrix · Answer

Take the area from z = - .833 to z = 0  --> .2967
Add the area from z = 0 onward (other half of area under curve)

.2967 + .5000 = .7967 which corresponds to a percentage of 79.7% expectation that the heights of 80 people randomly selected will be greater than 170 cm.

.7967*80 = 63.736 ==> about 64 people are expected to have heights exceeding 170 cm.