The probability that a randomly selected pregnancy lasts less than 188 days is approximately 0.3538. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 188 days. O B. If 100 pregnant individuals were selected independently from this population, we would expect 35 pregnancies to last less than 188 days. O C. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 188 days. (b) Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is = 194 and o; = 3.7712'. normal with u; (Round to four decimal places as needed.) (c) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 188 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 188 days is approximately .0558. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 independent random samples of size n = 18 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 188 days or less. O B If 100 indonondent random eomplne of eize - 12 nroanancins worn ohtained from thie nonulation wn unuld ovnont eamplelel to have acomplo moan of 188 dave or more
The probability that a randomly selected pregnancy lasts less than 188 days is approximately 0.3538. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 188 days. O B. If 100 pregnant individuals were selected independently from this population, we would expect 35 pregnancies to last less than 188 days. O C. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 188 days. (b) Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is = 194 and o; = 3.7712'. normal with u; (Round to four decimal places as needed.) (c) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 188 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 188 days is approximately .0558. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 independent random samples of size n = 18 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 188 days or less. O B If 100 indonondent random eomplne of eize - 12 nroanancins worn ohtained from thie nonulation wn unuld ovnont eamplelel to have acomplo moan of 188 dave or more
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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Transcribed Image Text:**Understanding the Distribution and Sampling of Pregnancy Lengths of a Certain Animal**
The lengths of pregnancies for a certain animal species are approximately normally distributed with a mean (\( \mu \)) of 194 days and a standard deviation (\( \sigma \)) of 16 days. Here’s a detailed analysis of this scenario through several statistical concepts:
### Probability and Interpretation
1. **Probability of Pregnancy Lengths**
- The probability that a randomly selected pregnancy lasts less than 188 days is approximately 0.3538.
2. **Interpreting the Probability**
- Choice B: If 100 pregnant individuals were selected independently from this population, we would expect 35 pregnancies to last less than 188 days.
### Sampling Distribution
- **Sample of 18 Pregnancies**
- We derive the sampling distribution of the sample mean length of pregnancies as:
- Normal distribution
- Mean (\( \mu_{\bar{x}} \)) = 194
- Standard deviation (\( \sigma_{\bar{x}} \)) = 3.7712
### Mean Gestation Period
1. **Probability of Sample Mean**
- The probability that the mean of a random sample of 18 pregnancies is less than 188 days is approximately 0.0558.
2. **Interpreting the Probability**
- It is identified that, based on 100 independent random samples of size \( n = 18 \), a specific number of samples are expected to have a mean gestation period of 188 days or less, though the exact number isn't filled in.
This information provides a comprehensive overview for calculating probabilities related to pregnancy durations and understanding sample distributions for a population of animals.
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