At a certain coffee​ shop, all the customers buy a cup of coffeeand some also buy a doughnut. The shop owner believes that thenumber of cups he sells each day is normally distributed with amean of 340 cups and a standard deviation of 18 cups. He alsobelieves that the number of doughnuts he sells each day isindependent of the coffee sales and is normally distributed with amean of 180 doughnuts and a standard deviation of 16.
a) The shop is open every day but Sunday. Assuming​ day-to-daysales are​ independent, what's the probability​ he'll sell over2000 cups of coffee in a​ week?
__________________ ​(Round to three decimal places as​needed.)
The daily exchange rates for the​ five-year period 2003 to 2008between currency A and currency B are well modeled by a normaldistribution with mean 1.798 in currency A​ (to currency​ B) andstandard deviation 0.047 in currency A. Given this​ model, andusing the​ 68-95-99.7 rule to approximate the probabilities ratherthan using technology to find the values more​ precisely, completeparts​ (a) through​ (d).
a) What would the cutoff rate be that would separate the highest16​% of currency​ A/currency B​ rates?
The cutoff rate would be ______________
​(Type an integer or a decimal rounded to the nearest thousandthas​ needed.)
The daily exchange rates for the​ five-year period 2003 to 2008between currency A and currency B are well modeled by a normaldistribution with mean 1.425 in currency A​ (to currency​ B) andstandard deviation 0.026 in currency A. Given this​ model, andusing the​ 68-95-99.7 rule to approximate the probabilities ratherthan using technology to find the values more​ precisely, completeparts​ (a) through​ (d).
​a) What is the probability that on a randomly selected dayduring this​ period, a unit of currency B was worth less than 1.425units of currency​ A?
The probability is _____________%
​(Type an integer or a​ decimal.)
