The weight of a certain packaged product has a mean of 5.2 kg and a standard deviation of 0.08 kg and follows a Normal distribution. If we drew a single package, what is the probability that the mean weight is over 5.3 kg?
mu <- 5.2
sigma <- 0.08
my.normal(mu, sigma, x1 = 5.3, label = "> 5.3kg")
(pnorm(5.3, mu, sigma, lower.tail = FALSE))
## [1] 0.1056498
What is the probability that the mean weight is under 5.3 kg?
my.normal(mu, sigma, x2 = 5.3, label = "< 5.3kg")
(pnorm(5.3, mu, sigma))
## [1] 0.8943502
Between 5.12 and 5.36 kg?
my.normal(mu, sigma, x1 = 5.12, x2 = 5.36, label = "5.12 to 5.36kg")
(pnorm(5.36, mu, sigma) - pnorm(5.12, mu, sigma))
## [1] 0.8185946