Final answer:
Part 1 (a): Approximately all 670 newborns weighed less than 5093 grams.
Part 2 (b): Approximately all 670 newborns weighed more than 2372 grams.
Part 3 (c): To estimate newborns between 3279 and 4186 grams, use Z-scores for these values and a standard normal distribution to find probabilities, then multiply by 670 for the estimated number.
Step-by-step explanation:
To estimate the number of newborns based on birth weights, we can use the Z-score formula and the standard normal distribution. The Z-score is calculated as:
Z= X−μ/σ
where:
- X is the individual data point,
- μ is the mean of the distribution,
- σ is the standard deviation.
The Z-score indicates how many standard deviations a data point is from the mean. We can then use a standard normal distribution table or a calculator to find the corresponding probabilities.
Let's calculate the estimates for each part:
- Part 1 (a):
Z5093 = 5093−3279/ 907
Use the Z-score to find the probability that a birth weight is less than 5093.
2. Part 2 (b):
Z2372 = 2372−3279/ 907
Use the Z-score to find the probability that a birth weight is greater than 2372.
3. Part 3 (c):
Z3279 = 3279−3279/ 907
Z4186 = 4186−3279/ 907
Use the Z-scores to find the probability that a birth weight is between 3279 and 4186.
Once you have the probabilities, you can estimate the number of newborns by multiplying each probability by the total number of newborns (670).
Please note that using a standard normal distribution table or a calculator is required for accurate probability values.
Your correct question is: Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 670 babies born in New York. The mean weight was 3279 grams with a standard deviation of 907 grams. Assume that birth weight data are approximately bell-shaped. Part 1 of 3 (a) Estimate the number of newborns whose weight was less than 5093 grams. of the 670 newborns weighed less than 5093 grams. Approximately Part 2 of 3 (b) Estimate the number of newborns whose weight was greater than 2372 grams. of the 670 newborns weighed more than 2372 grams. Approximately Part 3 of 3 (c) Estimate the number of newborns whose weight was between 3279 and 4186 grams. of the 670 newborns weighed between 3279 and 4186 grams. Approximately