Question 1200840
mean is 14.3
sandard deviation is 1.7
sample size is 12.
standard error is 1.7 / sqrt(12) = .4907477288.
probability that their mean length is less than 14.2 would be .4193 using the online calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = _blank">https://davidmlane.com/hyperstat/z_table.html</a>
the probability is .4192663762 using the ti-84 plus scientific calculator.
here's what the results look like using the online calculator.


<img src = "http://theo.x10hosting.com/2023/040902.jpg">


the key is that you have to use the standard error, rather than the standard deviation, because you are looking for the mean of a sample of size greater than 1.