Question

Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.3 pounds and standard deviation 3.8 pounds . Use the TI-83 Plus/TI-84 Plus calculator to answer the following. Round the answers to four decimal places. Part 1 of 4 (a) What proportion of babies weigh more than 14 pounds ? The proportion of babies weighing more than 14 pounds is 0.3273 . Part 2 of 4 (b) What proportion of babies weigh less than 16 pounds ? The proportion of babies weighing less than 16 pounds is .16510 . Part: 2 / 4 2 of 4 Parts Complete Part 3 of 4 (c) What proportion of babies weigh between 10 and 15 pounds ? The proportion of babies weighing between 10 and 15 pounds is .9662 .

Answer 1

To find the proportion of babies weighing more than 14 pounds, calculate the z-score corresponding to 14 pounds and find the area under the normal distribution curve to the right of that z-score. The proportion is approximately 0.3273.

Step-by-step explanation:

To find the proportion of babies weighing more than 14 pounds, we need to calculate the z-score corresponding to the weight of 14 pounds and find the area under the normal distribution curve to the right of that z-score.

Using the formula for z-score:

z = (x - μ) / σ

where x is the value (weight), μ is the mean weight, and σ is the standard deviation, we substitute the given values:

z = (14 - 12.3) / 3.8 = 0.4474

Using the TI-83 Plus/TI-84 Plus calculator or a standard normal distribution table, we find that the proportion of babies weighing more than 14 pounds is approximately 0.3273.