Question

A variable, X , is normally distributed with a mean of 125 and a standard deviation of 9 What percentage of values are greater than 127.5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the percentage of values that are greater than 127.5, we need to find the area under the normal curve to the right of 127.5.

First, we need to calculate the z-score for 127.5.

The z-score formula is given by:
z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

Substituting in the given values:
z = (127.5 - 125) / 9 = 2.5 / 9 ≈ 0.2778

Next, we can use a standard normal distribution table or calculator to find the area to the right of this z-score.

By looking up 0.2778 in the z-table, the corresponding area is 0.3938.

Therefore, the percentage of values greater than 127.5 is approximately 39.38%.