Using Excel to Compute Normal, Poisson, and Binomial probabilities

Question

I have been given a piece of work 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 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!

Answer 1

There are two issues here. (1) Are answers correct? (2) How to implement in Excel?

I will check your answers using R statistical software, and perhaps someone who uses Excel can comment on your use of Excel.

$A.$ $X \sim Norm(\mu=75, \sigma=15).$ Find $P(70 < X \le 90).$

diff(pnorm(c(70,90), 75, 15))
## 0.4719034

$B.$ $Y \sim Pois(\lambda = 1.5),$ where $\lambda = 1.5$ is the rate per hour. Find $P(Y \le 5).$

ppois(5, 5.5)
## 0.5289187

$C.$ First version: $V \sim Binom(5, .43).$ Find $P(V \le 2).$

Second version: $W \sim Binom(6, .43).$ Find $P(W \le 2).$

I share your puzzlement. I have no idea which problem you are being asked to solve.

pbinom(2, 5,.43)
## 0.6295451
pbinom(2, 6,.43)
## 0.4823037

Because your answers are correct and the Excel codes seem sensible (even though I wonder what the TRUEs are for), I would guess you must be using Excel correctly. Hope this much helps.

Note: It's a good thing each question says explicitly which kind of probability distribution to use, because the choice is not obvious from the situation: time to mark out a plot not obviously normal; cleared roots not obviously random Poisson events; finding species not obviously independent equally likely 'trials'.