To find the number of males from the new sample, we first need to compute for the z-score as shown below.
[tex] Z = \frac{\chi - \mu}{\sigma} [/tex]
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.
[tex] Z = \frac{164 - 170}{6} [/tex]
[tex] Z = -1 [/tex]
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.
Answer: 1010
