Questions: Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. (a) Find the 79th percentile of the baby weights. (b) Find the 8th percentile of the baby weights. (c) Find the first quartile of the baby weights. Use the π-84 plus calculator and round the answers to at least two decimal places. Part 1 of 3 The 79th percentile of the baby weights is pounds. Part 2 of 3 The 8th percentile of the baby weights is pounds. Part 3 of 3 The first quartile of the baby weights is pounds.

Solution Steps

To find the 79th percentile of the baby weights, we use the formula for the percentile in a normal distribution:

\[ P(X \leq x) = 0.79 \]

Using the mean \( \mu = 11.5 \) pounds and standard deviation \( \sigma = 2.7 \) pounds, we find:

\[ x_{79} = \mu + z_{0.79} \cdot \sigma \]

Calculating this gives:

\[ x_{79} \approx 13.68 \text{ pounds} \]

Next, we calculate the 8th percentile using a similar approach:

\[ P(X \leq x) = 0.08 \]

Again, using the mean and standard deviation:

\[ x_{8} = \mu + z_{0.08} \cdot \sigma \]

This results in:

\[ x_{8} \approx 7.71 \text{ pounds} \]

Finally, we find the first quartile (25th percentile):

\[ P(X \leq x) = 0.25 \]

Using the same parameters:

\[ x_{Q1} = \mu + z_{0.25} \cdot \sigma \]

This yields:

\[ x_{Q1} \approx 9.68 \text{ pounds} \]

Final Answer