### Understanding the Sampling DistributionSuppose a simple random sample of size $ n = 75 $ is obtained from a population whose size is $ N = 10,000 $ and whose population proportion with a specified characteristic is $ p = 0.6 $. Complete parts (a) through (c) below.#### (a) Describe the Sampling Distribution of $ \hat{p} $Choose the phrase that best describes the shape of the sampling distribution below:- **A.** Not normal because $ n \leq 0.05N $ and $ np(1 - p) $ < 10.- **B.** Approximately normal because $ n \leq 0.05N $ and $ np(1 - p) \geq 10 $.- **C.** Approximately normal because $ n \leq 0.05N $ and $ np(1 - p) < 10 $.- **D.** Not normal because $ n \leq 0.05N $ and $ np(1 - p) \geq 10 $.#### Determine the Mean of the Sampling Distribution of $ \hat{p} $\[ \mu_{\hat{p}} = p \](Round to one decimal place as needed.)#### Determine the Standard Deviation of the Sampling Distribution of $ \hat{p} $\[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \](Round to six decimal places as needed.)#### (b) Probability for $ x \geq 48 $ Individuals with the CharacteristicWhat is the probability of obtaining $ x = 48 $ or more individuals with the characteristic? That is, what is $ P(\hat{p} \geq 0.64) $?\[ P(\hat{p} \geq 0.64) = \] (Round to four decimal places as needed.)#### (c) Probability for $ x \leq 39 $ Individuals with the CharacteristicWhat is the probability of obtaining $ x = 39 $ or fewer individuals with the characteristic? That is, what is $ P(\hat{p} \leq 0.52) $?\[ P(\hat{p} \leq 0.52) = \] (Round to four

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Answered: Suppose a simple random sample of size…

Suppose a simple random sample of size n= 75 is obtained from a popula specified characteristic is p = 0.6. Complete parts (a) through (c) below.

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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Question

### Understanding the Sampling Distribution

Suppose a simple random sample of size $ n = 75 $ is obtained from a population whose size is $ N = 10,000 $ and whose population proportion with a specified characteristic is $ p = 0.6 $. Complete parts (a) through (c) below.

#### (a) Describe the Sampling Distribution of $ \hat{p} $
Choose the phrase that best describes the shape of the sampling distribution below:

- **A.** Not normal because $ n \leq 0.05N $ and $ np(1 - p) $ < 10.
- **B.** Approximately normal because $ n \leq 0.05N $ and $ np(1 - p) \geq 10 $.
- **C.** Approximately normal because $ n \leq 0.05N $ and $ np(1 - p) < 10 $.
- **D.** Not normal because $ n \leq 0.05N $ and $ np(1 - p) \geq 10 $.

#### Determine the Mean of the Sampling Distribution of $ \hat{p} $

\[ \mu_{\hat{p}} = p \]

(Round to one decimal place as needed.)

#### Determine the Standard Deviation of the Sampling Distribution of $ \hat{p} $

\[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \]

(Round to six decimal places as needed.)

#### (b) Probability for $ x \geq 48 $ Individuals with the Characteristic
What is the probability of obtaining $ x = 48 $ or more individuals with the characteristic? That is, what is $ P(\hat{p} \geq 0.64) $?

\[ P(\hat{p} \geq 0.64) = \] (Round to four decimal places as needed.)

#### (c) Probability for $ x \leq 39 $ Individuals with the Characteristic
What is the probability of obtaining $ x = 39 $ or fewer individuals with the characteristic? That is, what is $ P(\hat{p} \leq 0.52) $?

\[ P(\hat{p} \leq 0.52) = \] (Round to four

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