# define dataset

data_A <- rnorm(100. 80. 10)     # randomly create population dataset

data_B <- rnorm(100. 400. 100)   # randomly create population dataset

hist(data_A) #histogram

hist(data_B) #histogram

#Calculate population mean and standard deviation

A_data_std <- sd(data_A)*sqrt((length(data_A)-1)/(length(data_A)))

A_data_mean <- mean(data_A)

B_data_std <- sd(data_B)*sqrt((length(data_B)-1)/(length(data_B)))

B_data_mean <- mean(data_B)

# Provided that A got 92 and B got 610

A_obs <- 92

B_obs <- 610

A_Z_score <-  (A_obs - A_data_mean) / A_data_std

B_Z_score <-  (B_obs - B_data_mean) / B_data_std

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