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?
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.