Weights of 2 year old girls are normally distributed with a mean of 25.7 lbs and a standard deviation of 1.32 lbs. According to this information, what weight would be in the 33rd percentile?

1 answer

To find the weight that would be in the 33rd percentile, we need to find the corresponding z-score and then use that to find the weight from the z-score.

First, we find the z-score using the standard normal distribution formula:

z = (x - μ) / σ

where x is the weight we want to find, μ is the mean weight, and σ is the standard deviation.

Re-arranging the formula to solve for x, we get:

x = z * σ + μ

To find the z-score for the 33rd percentile, we can use a standard normal distribution table or calculator. The z-score corresponding to the 33rd percentile is approximately -0.44.

Plugging in the values, we get:

x = -0.44 * 1.32 + 25.7
x ≈ 24.99

Therefore, a weight of approximately 24.99 lbs would be in the 33rd percentile for 2 year old girls with a mean weight of 25.7 lbs and a standard deviation of 1.32 lbs.