Assignment 3

1. Calculate the probability of finding a tree with a dbh of 90 or greater based on the sample mean and sample standard deviation above. What is the z-score associated with a dbh of 90 cm? Include commands used to generate the answer. (out of 3)

• 1 mark for the code
• 1 marks for z-score and mentioning it
• 1 mark for the final probability

x <- c(272,272,236,154,256,156,143,269,205,175)
dbh <- x/pi

pnorm(q=90, mean = mean(dbh), sd=sd(dbh), lower.tail = FALSE) # method 1

## [1] 0.09809276

# using the second method 
z_score <- (90 - mean(dbh)) / sd(dbh)
pnorm(z_score, lower.tail=FALSE)

## [1] 0.09809276

2. Create a new dataset with a mean and standard deviation of your choosing and a sample size of 100. Plot the histogram being sure to label axes appropriately. (out of 3)

• 1 mark for the code
• 2 mark for the final histogram

sample_mean <- 10
sample_sd <- 2.5
sim_x <- rnorm(n=100, mean=sample_mean, sd=sample_sd)
hist(sim_x, xlab = "Title", main="")

3. Do you think the sample of trees we collected was representative of the wider forest? What would be some potential issues with inferring characteristics of the forest from this dataset? (out of 4)

Students should discuss the impact of sample size, sampling method and measurment errors and accuracy in the study