Question

An ice cream scoop holds a normally distributed mass of ice cream with an average of 68 g and variance of 16 g2 . In the freezer I have a 2 gallon bucket of ice cream4 . Because at such large volumes the dispensing process is inaccurate, the 2-gallon buckets also have a normally distributed mass with a mean of 4500 g and a standard deviation equal to 5% of the mean. 15. On Sunday, I make myself a 3-scoop ice cream sundae. What is the probability that it weighs more than 210 g? (consider only mass of ice cream; ignore the toppings)

16. I get easily bored and weigh a single scoop. What is the probability it has a mass less than 60 g?

17. Still bored, I weigh scoops from five days and take their average. What is the probability that the 5-day average is less than 65 g?

18. If I limit myself to 1 single scoop of ice cream per day, what is the expected mass of ice cream remaining in the 2-gallon bucket after 2 weeks (14 days) of eating ice cream?

19. If I limit myself to 1 single scoop of ice cream per day, what is the probability that my bucket lasts 60 or fewer days?

20. If I limit myself to 1 single scoop of ice cream per day, what is the probability that my bucket lasts more than 70 days?

Answer 1