1. Squirrels are nuts!

From what I have been told, squirrels spend six hours each day, seven days per week for the entire month of September searching randomly for nuts and they only find about one 'good nut' per 30 min - what makes a 'good nut' is hard to say, but apparently, squirrels intuitively know these things.

In any case, after they finish collecting their good nuts for the day, they hide them for the winter. The thing is, squirrels are not too smart and often forget where they hid their nuts. When the winter comes, they only have a 60% chance of finding any particular nut they have hidden. Since squirrels are very particular about their nuts, they will only find and eat the nuts they hid themselves.

The number of nuts a squirrel needs to eat to survive the winter depends on how cold it gets on any particular day. The number they need on any given day from January 1 to March 20 has a mean of 2 and a standard deviation of 0.25.

It is tough being a squirrel.

Some possibly useful information:

- Squirrels can eat partial nuts and save the rest for later.

- For the purposes of this question, you may assume all random variables are independent of each other.For example, the number of nuts required on January 1 is independent of those for any other day, like, say, January 2.

- Squirrels in Kingston have been seen driving pickup trucks.

- I really know nothing about squirrels, I made this all up.

a. Is the independence assumption on the number of nuts a squirrel requires per day on a reasonable one? Explain why / why not.

b. It is the morning of Feb 13, 2022 as I write this how many nuts does a squirrel need to have a 99% chance of surviving until the end of day March 19 (Report number rounded to 4 or more decimal places)?

c. How likely is it that a squirrel will collect at least 200 nuts?

d. Suppose a squirrel needs to eat 270 nuts to survive the entire winter. If it initially collected 460 nuts, will it survive the winter?

l. Squirrels are nuts! From what I have been told, squirrels spend six hours each day, seven days per week for the entire month of September searching randomly for nuts and they only find about one 'good nut' per 30 min what makes a 'good nut'r is hard to say, but apparently, squirrels intuitively know these things- In any case, after they finish collecting their good nuts for the day, they hide them for the winter. The thing is, squirrels are not too smart and often forget where they hid their nuts. When the winter comes, they only have a 60% chance of finding any particular nut they have hidden- Since squirrels are very particular about their nuts, they will only find and eat the nuts they hid themselves. The number of nuts a squirrel needs to eat to survive the winter depends on how cold it gets on any particular day. The number they need on any given day from January 1 to March 20 has a mean of 2 and a standard deviation of 0.25. It is tough being a squirrel. Some possibly useful information: Squirrels can eat partial nuts and save the rest for later. For the purposes of this question, you may assume all random variables are independent of each other- For example, the number of nuts required on January 1 is independent of those for any other day, like, say, January 2. Squirrels in Kingston have been seen driving pickup trucks. I really know nothing about squirrels, I made this all up. a. Is the independence assumption on the number of nuts a squirrel requires per day on a reasonable one? Explain why / why not. b. It is the morning of Feb 13, 2022 as I write this how many nuts does a squirrel need to have a 99% chance of surviving until the end of day March 19 {Report number rounded to 4 or more decimal places)? c. How likely is it that a squirrel will collect at least 200 nuts? d. Suppose a squirrel needs to eat 2TB nuts to survive the entire winter. If it initially collected 460 nuts, will it survive the winter