The heights of a certain group of adult males was found to be normally distributed. the mean height is 170 cm with a standard deviation of 6 cm. in a group of 1200 of these males, about how many would be more than 164 cm tall?

To find the number of males from the new sample,  we first need to compute for the z-score as shown below.



where Χ is the mean height we want to check, μ is the expected mean of the height, δ is the standard deviation, and n is the number of samples. Since, we  have all of these information at hand, we can now compute for the z-score of the sample. 




Now, using the z-table, we can find its p-value which we'll be using to find the number of males. Since z-score is -1, we have P(z > 0.158655) = 1 - 0.158655 = 0.841345. 

This signifies the percent of the total population that has a height of more than 164. So, out of 1200, we have 0.841345(1200) = 1009.614 ≈ 1010.

Therefore, we've seen that there are approximately 1010 male from the sample that will have a height of more than 164.

1010

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