Question 1204474
mean is 72 beats per minute.
standard deviation is 9 beats per minute (supposed).


probabiiity that a random person has over 77 beats per minue = .2893.


probbility that the mean of a random sample has over 77 beats per minute = .0092.


here are the resuts, using the calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


<img src = "http://theo.x10hosting.com/2023/102401.jpg">


<img src = "http://theo.x10hosting.com/2023/102402.jpg">


the differnce is that, for an individual sample, the standard deviation is used, while for the mean of a random sample, the standard error is used.


standard error = standard deviation / square root of sample size = 9 / sqrt(18) = 2.1213.


the standard error is defined as the standard deviation of the distribution of sample means.
this is different than the distribution of individual samples.
as the size of the sample gets larger, the standard error gets smaller.