What formula is used to find the x value (random variable) in a normal distribution, given the mean, z-score, and standard deviation?

x = mean + (z-score * standard deviation)

In a normal distribution of women's heights, the mean is 64 inches and the standard deviation is 3 inches. If a woman is in the top 5th percentile, would you expect her height to be above or below 64 inches? Explain.

Above 64 inches. The top percentile indicates a value greater than the mean.

Most standard normal tables provide the area to the left of a given z-score, not the area to the right.

Positive. 70% is greater than 50%, so the value is above the mean.

A negative z-score because 15% is less than 50%.

I can determine the value of x corresponding to a given probability in a normal distribution.

1
To find the x value (random variable) for a normal distribution, you can use the formula: x = mean + (z-score × standard deviation).
2
If you are looking for the top tenth percentile, you need to find the z-score that corresponds to an area of 0.9 to the left in the normal table.
3
When finding the heights equidistant from the mean that contain 88% of the population, you need to find the z-scores that correspond to 0.06 in each tail (above and below the mean).