Which command will calculate P(X>1.2) when X∼N(3,4)?

To calculate P(X>1.2) when X follows a normal distribution with mean 3 and variance 4 (standard deviation 2), you can use statistical software or programming languages like R or Python. Here's how you can do it in both:

1. In R:

   • First, standardize the value 1.2 using the formula Z = (X - μ) / σ. Here, X = 1.2, μ = 3, and σ = 2 (the square root of the variance). So, Z = (1.2 - 3) / 2 = -0.9.
   • Then, use the pnorm function to find the probability that a standard normal random variable is less than -0.9. This gives P(X<1.2).
   • Finally, subtract this from 1 to get P(X>1.2), because P(X>1.2) = 1 - P(X<1.2).
   • The R command would be: 1 - pnorm(-0.9)

2. In Python:

   • You can use the scipy.stats library, which has a function called norm for working with normal distributions.
   • Similar to R, first standardize the value 1.2 to get Z = -0.9.
   • Then, use the norm.cdf function to find P(X<1.2), and subtract this from 1 to get P(X>1.2).
   • The Python command would be: 1 - scipy.stats.norm.cdf(-0.9)

Remember, these commands give the probability that a random variable from the given normal distribution is greater than 1.2.