Question 1186190
population mean = 140.
population standard deviation = 30
sample size = 75


when you are dealing with the mean of a sample, you need to use the standard error.


standard error = standard deviation divided by square root of smaple size = 30 / sqrt(75) = 3.4641 rounded to 4 decimal places.


probability that the sample mean will be between 132 and 136 is is equal to .1136 = 11.36%.


calculator used can be found at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


here's a display of the results from using that calculator.


<img src = "http://theo.x10hosting.com/2021/101804.jpg" >