The length of Paulo’s lunch break follows a normal distribution with mean µ minutes and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes.
(i) Find the value of µ.
(ii) Find the probability that Paulo’s lunch break lasts for between 40 and 46 minutes on every one of the next four days.

Question

The length of Paulo’s lunch break follows a normal distribution with mean µ minutes and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes. 
(i) Find the value of µ.
(ii) Find the probability that Paulo’s lunch break lasts for between 40 and 46 minutes on every one of the next four days.

anonymous · Answer

http://qlx.is.quoracdn.net/main-30481a663b03bbd7.png You know that your p-value for "more than 52 minutes" is one in four, or 0.25; since it lasts "more than" 52 minutes, that means the area is 0.25 to the right. Since most z-tables are constructed to the left, you'll want to convert this to an area of 0.75 to the left.