Question

1. the birth weight of children born in the us is said to have an approximately normal distribution. in 2021, the mean birth weight of an infant was 7.5 pounds (lb.) with a standard deviation of 1.5 lb. the normal curve modeling this distribution is shown with the values along the x-axis unlabeled. the vertical line in the center marks the mean, with each vertical line to the right or left representing a standard deviation from the mean. image of normal curve with 68%, 95%, 99.7% and unlabeled x-axis boxes, mean at center a. label the center of the distribution with the mean value of 7.5

Explanation:

Step1: Identify the mean position

The center of the normal distribution is the mean. Given the mean birth weight is 7.5 lb, the center (the middle box labeled "mean") should be labeled with 7.5.

Step2: Calculate values for other boxes (using mean ± n*standard deviation, n = 1,2,3)

• For n = 1 (left of mean): $7.5 - 1.5 = 6.0$; (right of mean): $7.5 + 1.5 = 9.0$
• For n = 2 (left of mean): $7.5 - 2*1.5 = 7.5 - 3.0 = 4.5$; (right of mean): $7.5 + 2*1.5 = 7.5 + 3.0 = 10.5$
• For n = 3 (left of mean): $7.5 - 3*1.5 = 7.5 - 4.5 = 3.0$; (right of mean): $7.5 + 3*1.5 = 7.5 + 4.5 = 12.0$

From left to right (assuming the boxes are ordered from leftmost to rightmost, with the middle being the mean):

1. Leftmost (n = 3 left): 3.0
2. Next (n = 2 left): 4.5
3. Next (n = 1 left): 6.0
4. Middle (mean): 7.5
5. Next (n = 1 right): 9.0
6. Next (n = 2 right): 10.5
7. Rightmost (n = 3 right): 12.0

(For part a, just label the center box with 7.5 as it's the mean.)

Answer:

For part a, the center (middle box labeled "mean") is labeled with 7.5.

(If we consider labeling all boxes, from left to right: 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, 12.0)