MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Hi, I need help solving part F. Thanks!

**Homework: 2-2 MyStatLab: Module Two Problem Set**

**Score:** 4.58 of 5 pts
**Progress:** 11 of 15 (15 complete)

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### Problem 8.1.19-T

**Instructions:** 
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with a mean (μ) of 281 days and a standard deviation (σ) of 21 days. Complete parts (a) through (f) below.

**(a)** What is the probability that a randomly selected pregnancy lasts less than 274 days?

- The probability that a randomly selected pregnancy lasts less than 274 days is approximately **0.3694**. (Round to four decimal places as needed.)
  
  **Interpret this probability:**
  - If 100 pregnant individuals were selected independently from this population, we would expect **37** pregnancies to last less than 274 days. (Correct selection)

**(b)** Suppose a random sample of 23 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

- The sampling distribution of \( \bar{X} \) is **normal** with \( \mu_{\bar{x}} = 281 \) and \( \sigma_{\bar{x}} = 4.3788 \). (Round to four decimal places as needed.)

**(c)** What is the probability that a random sample of 23 pregnancies has a mean gestation period of 274 days or less?

- The probability that the mean of a random sample of 23 pregnancies is less than 274 days is approximately **0.0550**. (Round to four decimal places as needed.)

  **Interpret this probability:**
  - If 100 independent random samples of size n = 23 pregnancies were obtained from this population, we would expect **6** sample(s) to have a sample mean of 274 days or less. (Correct selection)

**(d)** What is the probability that a random sample of 50 pregnancies has a mean gestation period of 274 days or less?

- The probability that the mean of a random sample of 50 pregnancies is less than 274 days is approximately **0.0092**. (Round to four decimal places as needed.)

  **Interpret this probability:**
  - If 100 independent random samples of size n = 50 pregnancies were obtained from this population, we would expect **1** sample
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Transcribed Image Text:**Homework: 2-2 MyStatLab: Module Two Problem Set** **Score:** 4.58 of 5 pts **Progress:** 11 of 15 (15 complete) --- ### Problem 8.1.19-T **Instructions:** Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with a mean (μ) of 281 days and a standard deviation (σ) of 21 days. Complete parts (a) through (f) below. **(a)** What is the probability that a randomly selected pregnancy lasts less than 274 days? - The probability that a randomly selected pregnancy lasts less than 274 days is approximately **0.3694**. (Round to four decimal places as needed.) **Interpret this probability:** - If 100 pregnant individuals were selected independently from this population, we would expect **37** pregnancies to last less than 274 days. (Correct selection) **(b)** Suppose a random sample of 23 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. - The sampling distribution of \( \bar{X} \) is **normal** with \( \mu_{\bar{x}} = 281 \) and \( \sigma_{\bar{x}} = 4.3788 \). (Round to four decimal places as needed.) **(c)** What is the probability that a random sample of 23 pregnancies has a mean gestation period of 274 days or less? - The probability that the mean of a random sample of 23 pregnancies is less than 274 days is approximately **0.0550**. (Round to four decimal places as needed.) **Interpret this probability:** - If 100 independent random samples of size n = 23 pregnancies were obtained from this population, we would expect **6** sample(s) to have a sample mean of 274 days or less. (Correct selection) **(d)** What is the probability that a random sample of 50 pregnancies has a mean gestation period of 274 days or less? - The probability that the mean of a random sample of 50 pregnancies is less than 274 days is approximately **0.0092**. (Round to four decimal places as needed.) **Interpret this probability:** - If 100 independent random samples of size n = 50 pregnancies were obtained from this population, we would expect **1** sample
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