Question

At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 340 cups and a standard deviation of 18 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 180 doughnuts and a standard deviation of 16.

a) The shop is open every day but Sunday. Assuming​ day-to-day sales are​ independent, what's the probability​ he'll sell over 2000 cups of coffee in a​ week?

__________________ ​(Round to three decimal places as​ needed.)

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.798 in currency A​ (to currency​ B) and standard deviation 0.047 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

a) What would the cutoff rate be that would separate the highest 16​% of currency​ A/currency B​ rates?

The cutoff rate would be ______________

​(Type an integer or a decimal rounded to the nearest thousandth as​ needed.)

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.425 in currency A​ (to currency​ B) and standard deviation 0.026 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

​a) What is the probability that on a randomly selected day during this​ period, a unit of currency B was worth less than 1.425 units of currency​ A?

The probability is _____________%

​(Type an integer or a​ decimal.)

Answer 1

At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 340 cups and a standard deviation of 18 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 180 doughnuts and a standard deviation of 16.

a) The shop is open every day but Sunday. Assuming​ day-to-day sales are​ independent, what's the probability​ he'll sell over 2000 cups of coffee in a​ week?

__________________ ​(Round to three decimal places as​ needed.)

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.798 in currency A​ (to currency​ B) and standard deviation 0.047 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

a) What would the cutoff rate be that would separate the highest 16​% of currency​ A/currency B​ rates?

The cutoff rate would be ______________

​(Type an integer or a decimal rounded to the nearest thousandth as​ needed.)

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.425 in currency A​ (to currency​ B) and standard deviation 0.026 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

​a) What is the probability that on a randomly selected day during this​ period, a unit of currency B was worth less than 1.425 units of currency​ A?

The probability is _____________%

​(Type an integer or a​ decimal.)