Question

The weights for 12-month-old males are normally distributed with a mean of 22.9 pounds and a standard deviation of 2.2 pounds. Use the given table to find the

percentage of 12-month-old males who weigh more than 27.3 pounds.

Answer 1

To find the percentage of 12-month-old males weighing over 27.3 pounds, calculate the z-score and consult a normal distribution table. The z-score corresponding to 27.3 pounds is 2, which indicates that approximately 2.5% of 12-month-old males weigh more than 27.3 pounds.

Step-by-step explanation:

To calculate the percentage of 12-month-old males who weigh more than 27.3 pounds when the weights are normally distributed with a mean of 22.9 pounds and a standard deviation of 2.2 pounds, we need to follow these steps:

1. First, calculate the z-score of 27.3 pounds using the formula:
   Z = (X - μ) / σ
   where X is the weight of interest (27.3 pounds), μ is the mean (22.9 pounds), and σ is the standard deviation (2.2 pounds).
2. Substitute the values:
   Z = (27.3 - 22.9) / 2.2
   Z = 4.4 / 2.2
   Z = 2
3. Consult a standard normal distribution table to find the proportion of the area to the right of a z-score of 2.
4. Typically, a z-score of 2 corresponds to the 97.5th percentile of the normal distribution, meaning that 97.5% of values lie below this z-score. Therefore, 100% - 97.5% = 2.5% of 12-month-old males weigh more than 27.3 pounds.