Answer :
Finding the proportion is the same as finding the following probability:
[tex]P(X\ge77)[/tex]in a normal distribution with mean 90 and standard deviation 10. To find this probability we use the z-score, defined by:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where x is the value we need (in this case x=77), hence the probability we are looking for can be calculated as:
[tex]P(X\ge77)=P(Z\ge\frac{77-90}{10})=P(Z\ge-1.3)[/tex]Using the tables of a normal distribution we have that:
[tex]P(Z\ge-1.3)=0.9032[/tex]Hence:
[tex]P(X\ge77)=0.9032[/tex]Therefore, 90.32% of tax forms will be completed in more than 77 minutes.
