A lake has a water level which is used to determine if watering restrictions need to be implemented for the neighboring city.
A lake has a water level which is used to determine if watering restrictions need to be implemented for the neighboring city. Water levels are measured on a weekly basis, and restrictions are placed if the lake level drops below 1060 ft. Weekly water levels are normally distributed with and mean of 1070 ft, and a standard deviation of 4.5 ft.
1) In a given year (52 weeks), what is the probability that there will be watering restrictions for 2 or more weeks? 3 or more weeks?
2) What is the probability tht the water level will drop below 1053.3 ft at least once in the next 10 years (521 weeks)?
3) How many weeks must pass before the likelihood of the lake water level falling below 1053.3 ft at least twice more is 0.90?