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June 2017 p63 q4
3136
The random variable X has the distribution \(N(\mu, \sigma^2)\), where \(\mu = 1.5\sigma\). A random value of \(X\) is chosen. Find the probability that this value of \(X\) is greater than 0.
Solution
To find \(P(X > 0)\), we standardize the variable using the formula for the standard normal distribution: