The number of hits per day on the Web site of a tool company is normally distributed with a mean of $500$ and a standard deviation of $120.$

a$.$ What proportion of days have more than $620$ hits?

b$.$ What proportion of days have between $540$ and $620$ hits?

c$.$ Find the number of hits such that only $15\%$ of the days will have the number of hits below this number.

Click the icon to view the standard normal table of the cumulative distribution function.

a$.$ The proportion of days with more than $620$ hits is $($Round to four decimal places as needed.$)$