Final answer:
To find the percentiles and quartile of baby weights, we need to convert the weights to z-scores using the formula z = (x - mean) / standard deviation. Using the TI-84 Plus calculator, we can then find the corresponding percentiles and quartile from the standard normal distribution. The 84th percentile of baby weights is approximately 3.779 pounds, the 11th percentile is approximately 7.476 pounds, and the third quartile is approximately 15.07 pounds.
Step-by-step explanation:
To find the percentiles and quartile of baby weights, we need to convert the weights to z-scores using the formula:
z = (x - mean) / standard deviation
Using the TI-84 Plus calculator, we can then find the corresponding percentiles and quartile from the standard normal distribution.
(a) The z-score for the 84th percentile can be found by using invNorm(0.84) which gives us a z-score of approximately 0.994.
We can then use the formula z = (x - mean) / standard deviation to solve for x: 0.994 = (x - 12.3) / 3.8. Solving for x, we get x ≈ 3.779.
Therefore, the 84th percentile of baby weights is approximately 3.779 pounds.
(b) The z-score for the 11th percentile can be found by using invNorm(0.11) which gives us a z-score of approximately -1.215. Using the formula z = (x - mean) / standard deviation and plugging in the values, we get -1.215 = (x - 12.3) / 3.8. Solving for x, we get x ≈ 7.476.
Therefore, the 11th percentile of baby weights is approximately 7.476 pounds.
(c) The third quartile corresponds to the 75th percentile. Using invNorm(0.75), we find that the z-score is approximately 0.674.
Using the formula z = (x - mean) / standard deviation, we get 0.674 = (x - 12.3) / 3.8. Solving for x, we get x ≈ 15.07.
Therefore, the third quartile of baby weights is approximately 15.07 pounds.