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)---### 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

Name: Hi, I need help solving part F. Thanks! **Homework: 2-2 MyStatLab: Mod
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Description: 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)---### Problem 8.1.19-T**Instructions:** Suppose the lengths of the pregnancies of a certain animal

Given Information: μ=281 and σ=21 (f) To find the probability that a random sample of size 19 will have a mean gestation period within 9 days of the mean: Mean of X¯ is given as μx¯=μ=281 Standard deviation is given as: σx¯=σn=2119=4.818 Z-score is a measure which tells how many standard deviations away, a data value is, from the mean. It is given by the formula: Z=X-μσRequired probability is obtained as follows: P272<X¯<290=PX¯<290-PX¯<272=PZ<290-2814.818-PZ<272-2814.818=PZ<1.87-P-1.87=0.96926-0.03074 [Using a standard normal table]=0.93852 Therefore, probability that a random sample of size 19 will have a mean gestation period within 9 days of the mean is 0.9385

Math

Statistics

(f) What is the probability a random sample of size 19 will have a mean gestation period within 9 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 9 days of the mean is (Round to four decimal places as needed.)

(f) What is the probability a random sample of size 19 will have a mean gestation period within 9 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 9 days of the mean is (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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)

---

### 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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