Based on data from the National Center for Health Statistics, N. Wetzel used the normal distribution to model the length of gestation for pregnant US woman ( Chance, Spring 2001). Gestation length has mean of 280 days with a standard deviation of 20 days.
a. Find the probability that gestation length is between 275.5 and 276.5 days. (This estimates the probability that a woman has her baby 4 days earlier than the due date)
b. Find probability that gestation length is between 258.5 and 259.5 days. (This estimates the probability that a woman has her baby 21 days earlier than the due date).
c. Find the probability that gestation length is between 254.5 and 255.5 days. (This estimates the probability that a woman has her baby 25 days earlier than the due date.
d. The Chance article referenced a newspaper story about three sisters who all gave birth on the same day (March 11, 1998). Karralee had her baby 4 days early: Marrianne had her baby 21 days early: and Jennifer had her baby 25 days early. Use the results, parts a-c estimate the probability that all three woman have their babies 4, 21, 25 days early, respectively. Assume the births are independent events.
Tony/Jon/Lindsey -- please do not change names.
I did not change names I have two children in college and they had different questions ask before you blame
We have many people who change their names in here. There is NO way Ms. Sue could know that you are posting for two students, and you have presented with 3 names. It is not incumbent upon her to have to guess, or ask you anything. You did literally change names. She deserves an apology from you.
I wish I could help you with your question, but Stats are way beyond my injured brain's abilities. All I can suggest is, look at the article in question, it may have the probability numbers for d. in it, so your son can have an idea of how big it is and if his calculation is achieving a similar result.
To find the probabilities in each part, we will use the properties of the normal distribution. The normal distribution is characterized by its mean (µ) and standard deviation (σ).
a) We need to find the probability that gestation length is between 275.5 and 276.5 days, which estimates the probability that a woman has her baby 4 days earlier than the due date.
To find this probability, we will use the formula: P(a ≤ X ≤ b) = Φ((b-µ)/σ) - Φ((a-µ)/σ), where Φ(z) is the cumulative distribution function for the standard normal distribution.
1. Calculate the z-scores for the given values of a and b:
z1 = (275.5 - 280) / 20 = -0.225
z2 = (276.5 - 280) / 20 = -0.175
2. Use the z-scores to find the probabilities:
P(275.5 ≤ X ≤ 276.5) = Φ(-0.175) - Φ(-0.225)
You can look up the values of Φ(-0.175) and Φ(-0.225) in the standard normal distribution table, or use a calculator or statistical software to find the probabilities.
b) We need to find the probability that gestation length is between 258.5 and 259.5 days, which estimates the probability that a woman has her baby 21 days earlier than the due date.
Follow the same steps as in part a, but now use the values of 258.5 and 259.5 to calculate the z-scores.
c) We need to find the probability that gestation length is between 254.5 and 255.5 days, which estimates the probability that a woman has her baby 25 days earlier than the due date.
Follow the same steps as in part a, but now use the values of 254.5 and 255.5 to calculate the z-scores.
d) To estimate the probability that all three women have their babies 4, 21, and 25 days early, respectively, we can assume that the births are independent events. In this case, the probabilities can be multiplied together.
For example, the probability that all three women have their babies 4 days early is the product of the probabilities from part a for each woman individually.
Note: It's important to remember that the normal distribution is an approximation, and actual data may not perfectly follow this distribution. Also, these probabilities are estimates based on the assumptions made in the problem.