***[ Please do this in Rstudio (R code) ]*** Exercise 1: Based on weighting the

Question

***[ Please do this in Rstudio (R code) ]***

Exercise 1: Based on weighting the most animals in the population, the American Angus Association reported that mature Angus cows had a mean weight of 1309 pounds with a standard deviation of 157 pounds. A research randomly measures 100 mature Angus cows. Use R commands to answers the following questions. (a) Find the probability that the average weight of the 100 mature Angus cows is greater than 1320 pounds. (b) Find the probability that the average weight of the 100 mature Angus cows is between 1290 and 1310.

Explanation / Answer

(a) Find out the sample standard deviation of the mean

sample.sd <- 157/sqrt(100)

Assuming the population follows a normal distribution, the command for P(X > 1320) is

pnorm(1320,mean = 1309,sd = sample.sd,lower.tail = FALSE)
[1] 0.2417648

(For > sign, we use the option lower.tail = FALSE)

(b) P(1290 < X < 1310) = P(X < 1310) - P(X < 1290)

pnorm(1310,mean = 1309,sd = sample.sd) - pnorm(1290,mean = 1309,sd = sample.sd)
[1] 0.4122904

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