Question

The following require calculating the probability of the specified event based on an assumed probability distribution. Remember to consider whether the event involves discrete or continuous variables.

You are measuring height of vegetation in a grassland using a Robel pole and a 5 m. radius. Based on 100 random samples from the grassland, you obtain a mean height of 0.6 m with a standard deviation of 0.04 m2.

a) What distribution is the appropriate reference for this problem?

b) Ninety percent of the samples are expected to be under what height? Use you will need to use the appropriate command in R of d<dist>, p<dist>, q<dist>, or r<dist> and use the appropriate values as arguments. Use help(command) to find out what these arguments are for your distribution, e.g., help(qbinom) will give you the help for this command.

Answer 1

After taking samples for 100 grass in that grassland, I obtained the mean height of 0.6m and a standard deviation of 0.04 m2.

a). Here for the reference purpose, I can safely assume that the height of the grass will follow a normal distribution with mean 0.6m and sd 0.04m2.

b). Here to get the estimated height, I need to use the following code

qnorm(0.90,mean = 0.6, sd = 0.04)

which has given the following result:  0.6512621

So I can safely say that 90% of samples will fall under the height of 0.651m

Now for the learning of the commands

The Normal Distribution
Description
Density, distribution function, quantile function and random generation for the normal distribution with mean equal to mean and standard deviation equal to sd.

Usage
dnorm(x, mean = 0, sd = 1, log = FALSE)
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
rnorm(n, mean = 0, sd = 1)
Arguments
x, q  
vector of quantiles.

p  
vector of probabilities.

n  
number of observations. If length(n) > 1, the length is taken to be the number required.

mean  
vector of means.

sd  
vector of standard deviations.

log, log.p  
logical; if TRUE, probabilities p are given as log(p).

lower.tail  
logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].

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