Suppose X has a normal distribution with mean -0.72 and standard deviation \sqrt{2}. The pnorm(), dnorm() and qnorm() functions should be useful in the following.\na) What is the expected value of 3X + 5?\nb) What is the variance of 3X + 5?\nc) Calculate the probability X > 0\nd) Calculate the probability that X < -2.0\ne) Calculate the probability that -2.0 < X < 0.1\nf) If the probability that X > t = .241 then what is t?
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The pnorm() function calculates the cumulative probability up to a given value. Since we want the probability that X is greater than 3, we need to subtract the cumulative probability up to 3 from 1. The code to calculate this probability in R would be: ``` 1 - Show more…
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