#Realizar algunos cálculos de probabilidad haciendo uso de la Distribución Normal Estándard y mediante la función dnorm()

#Cargamos librerías

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#1. Encontar la probabildiad para cuando p(z≤1) con μ=0 y σ=1. Se usa pnorm() para encontrar probabilidad acumulada

pnorm(1, mean = 0, sd= 1)
## [1] 0.8413447

#Visualizar la distribución de probabilidad normal estándard para cuando μ=0 y σ=1

plotDist("norm", mean = 0, sd = 1, groups = x < 1, type = "h")

#2. Encontar la probabilidad para cuando p(0.50≤<≤1.25) con μ=0 y σ=1. Se usa pnorm() para encontrar probabilidad acumulada y restando p(1.25)−p(−0.50)

pnorm(1.25, mean = 0, sd= 1) -pnorm(-0.50, mean = 0, sd= 1)
## [1] 0.5858127

#Visualizar la distribución de probabilidad normal estándard para cuando μ=0 y σ=1

plotDist("norm", mean = 0, sd = 1, groups = x > -0.50 & x < 1.25, type = "h")

#3. Encontar la probabilidad para cuando p(z≥1.58) con μ=0y σ=1. Se usa pnorm() para encontrar probabilidad acumulada y restando p(1.25)−p(−0.50)

1 - pnorm(c(1.58), mean = 0, sd= 1)
## [1] 0.05705343
# ó bien

pnorm(c(1.58), mean = 0, sd= 1, lower.tail= F)
## [1] 0.05705343

#Visualizar la distribución de probabilidad normal estándard para cuando μ=0 y σ=1

plotDist("norm", mean = 0, sd = 1, groups = x > 1.58, type ="h")

#¿Cuál es la probabilidad de que la variable aleatoria X esté entre 10 y 14?

pnorm(2, mean=0,sd=1) - pnorm(0, mean=0,sd=1)
## [1] 0.4772499

#Ó en dado caso

pnorm(14, mean = 10, sd=2) - pnorm(10, mean = 10, sd=2)
## [1] 0.4772499