Suppose X ~ N(μ,σ ^2). Find the distribution of Z = (X - μ)/σ using one dimensional change of variable.
Also, find P(|Z| 1) using tables.

Question

Suppose X ~ N(μ,σ ^2). Find the distribution of Z = (X - μ)/σ using one dimensional change of variable.
Also, find P(|Z| > 1) using tables.

amistre64 · Answer

From what I can decipher, there is no question being asked for starters.

Suppose that [the data?] has a normal distribution with a given mean and variance.  Find the z-score (defined as (data - mean)/standard deviation ) using [one dimensional change of variables?]  Find the cumulated probability associated with a z-score greater than 1.

The empirical rule suggests that 68% of the date is within 1 standard deviation of the mean; so everything that is beyopnd a standard deviation of 1 is going to amount to around (100 - 68)%.