Suppose X is a normally distributed random variable with mean 0 and variance 1 (i. e., standard normal). Compute the following (Hint: you can use the R functions pnorm and qnorm to answer these questions).
P r(X < 1:96)
P r(X > 1:64)
P r(0:5 < X < 0:5) 1% quantile, q:01 and 99% quantile, q:99 ? 5% quantile, q:05 and 95% quantile,

Step-by-step explanation:

Given

--- Mean

--- Variance

Calculate the standard deviation

Solving (a): P(X < 1.96)

First, we calculate the z score using:

This gives:

The probability is then solved using:

From the standard normal distribution table

So:

Solving (b): P(X > 1.64)

First, we calculate the z score using:

This gives:

The probability is then solved using:

From the standard normal distribution table

So:

Solving (c): P(0.5 < X < 0.5)

This can be split as:

In probability:

becomes

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step-by-step explanation: