So I have been given a piece of work from my university in regards to using Excel to conduct certain probability finding questions. I will write the questions below and show you what I have done so far in hopes for someone to tell me if I am doing it right and help me understand where and how I may be going wrong!

The questions and their respective working is as follows:

**Part A**

Question: The time taken for field workers to mark out a plot for logging is normally distributed with a mean of 75 minutes and a standard deviation of 15 minutes. What is the probability that the time is between 70 and 90 minutes? (You need to use an appropriate Excel function to determine the probability.)

Answer: Through some research I found that the best way to go about doing this is by using the following normal distribution to calculate the probability and the formula i used is =NORM.DIST(90,75,15,TRUE)-NORM.DIST(70,75,15,TRUE). This gave me the probability of 47% (0.4719). Is this the correct way to go about answering this or am I doing it wrong?

**Part B**

Question: A logger knows that, on average, it takes two hours to clear eleven tree roots. Find the probability that a logger will clear at most five tree roots in a one hour period.

Answer: I followed a Poisson Distribution to calculate this using the equation =POISSON.DIST(5,5.5,TRUE) where I assume that since 11 is the average in 2 hours then 5.5 is the average in 1 hour, and from this I get a probability of 53% (0.5289). In this what I am wondering is that can mean be divided by two if the time is halved?

**Part C**

Question: the probability of finding a tree species with an extensive subterranean root system is 0.43 and five plots were selected, find the probability that at most two of the six plots contain a tree species with an extensive subterranean root system.

Answer: In this I used a Binomial Distribution with the equation BINOM.DIST(2,5,0.43,TRUE)=63% (0.6295) where I am telling excel that I wish to find out for 2 instances where previous experiment has had 0.43 probability from 5 plots. Here the confusion is the wording of the question where it says 2 out of 6 plots which makes me wonder if I am supposed to alter the data to be similar to the sample set of 5.

I hope that I am not too far off topic here and that I can hear back from someone soon as to if I am going in the right direction! Thank you for taking the time to look through this!