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# X ~ N(mean = 75, sd = 5) # pnorm is used to calculate the probability for a normal random variable # what is the P( X <= 70 ) pnorm(q = 70, mean = 75, sd = 5) pnorm(q = 85, mean = 75, sd = 5, lower.tail = F) #P(Z >= 1) pnorm(q = 1, mean = 0, sd = 1, lower.tail = F) # area above a z score is approx 16% #qnorm is used to calculate quartiles or percentiles for a random variable #find Q1 qnorm(p = 0.25, mean = 75, sd = 5, lower.tail = T) #dnorm is for calculatung the probability density function #first we create a sequence of X values that run from 55-95 X <- seq(from=55, to=95, by=0.25) dens <- dnorm(X, mean=75, sd=5)
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[1] 0.1586553 [1] 0.02275013 [1] 0.1586553 [1] 71.62755