Question 1185353
you can use the following normal distribution z-score calculator to solve this easily.


<a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


the first one gives you the probability it will take more than 51 minutes.


the second one gives you  the probability it will take less than 45 minutes.


<img src = "http://theo.x10hosting.com/2021/100202.jpg" >


<img src = "http://theo.x10hosting.com/2021/100203.jpg" >


this calculator can be used with z-scores and with raw scores.


with z-scores, the mean is 0 and the standard deviation is 1.


with raw scores, the mean and the standard deviation are what they are as given in the problem.


when you are dealing with sample means in samples whose size is greater than 1, then you need to use the standard error, rather than the standard deviation.


this problem did not require that.