k here to view the standard normal distribution table (page 1). k here to view the standard normal distribution table (page 2). Describe the sampling distribution of p. ose the phrase that best describes the shape of the sampling distribution below. A. Approximately normal because ns0.05N and np(1 - p) < 10. B. Not normal because ns0.05N and np(1 - p) < 10. c. Approximately normal becausens0.05N and np(1 - p) 2 10. D. Not normal because ns0.05N and np(1 -p) 2 10. ermine the mean of the sampling distribution of p. 0.2 (Round to one decimal place as needed.) ermine the standard deviation of the sampling distribution of p. 0.035777 (Round to six decimal places as needed.) What is the probability of obtaining x = 30 or more individuals with the characteristic? That is, what is P(p 2 0.24)?
k here to view the standard normal distribution table (page 1). k here to view the standard normal distribution table (page 2). Describe the sampling distribution of p. ose the phrase that best describes the shape of the sampling distribution below. A. Approximately normal because ns0.05N and np(1 - p) < 10. B. Not normal because ns0.05N and np(1 - p) < 10. c. Approximately normal becausens0.05N and np(1 - p) 2 10. D. Not normal because ns0.05N and np(1 -p) 2 10. ermine the mean of the sampling distribution of p. 0.2 (Round to one decimal place as needed.) ermine the standard deviation of the sampling distribution of p. 0.035777 (Round to six decimal places as needed.) What is the probability of obtaining x = 30 or more individuals with the characteristic? That is, what is P(p 2 0.24)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Answer parts A and C Only!
Transcribed Image Text:**Standard Normal Distribution Table**
The standard normal distribution is a key concept in statistics, representing a normal distribution with a mean of 0 and a standard deviation of 1. This table, often used in statistical analysis, provides the area (probability) to the left of a given z-score in a standard normal distribution.
### Explanation of Graphs
In both pages, a bell-shaped curve represents the standard normal distribution. The curve is symmetrical about the mean (z = 0). The shaded region to the left of a particular z-value represents the cumulative probability up to that z-value. The "Area" refers to this cumulative probability.
### Standard Normal Distribution Table (Page 1)
This table provides values of cumulative probabilities for negative z-scores from -3.4 to -0.1. The z-values are listed in the first column, with the first decimal place of the z-value across the top representing additional decimal places (0.00 to 0.09).
For example:
- For z = -2.5, the cumulative probability from the table is 0.0062.
### Standard Normal Distribution Table (Page 2)
This table displays values for positive z-scores from 0.0 to 3.4. Similar to page 1, the first column lists the z-scores, with additional decimal places across the top.
For example:
- For z = 1.5, the cumulative probability from the table is 0.9332.
These tables are crucial tools for finding probabilities and percentiles in data that follow a standard normal distribution.
![Suppose a simple random sample of size \( n = 125 \) is obtained from a population whose size is \( N = 25,000 \) and whose population proportion with a specified characteristic is \( p = 0.2 \).
[Click here to view the standard normal distribution table (page 1).]
[Click here to view the standard normal distribution table (page 2).]
---
**(a) Describe the sampling distribution of \( \hat{p} \).**
Choose the phrase that best describes the shape of the sampling distribution below.
- A. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).
- B. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).
- C. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).
- D. Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).
**Determine the mean of the sampling distribution of \( \hat{p} \).**
\( \mu_{\hat{p}} = 0.2 \) (Round to one decimal place as needed.)
**Determine the standard deviation of the sampling distribution of \( \hat{p} \).**
\( \sigma_{\hat{p}} = 0.035777 \) (Round to six decimal places as needed.)
---
**(b) What is the probability of obtaining \( x = 30 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.24) \)?**
\( P(\hat{p} \geq 0.24) = 0.1318 \) (Round to four decimal places as needed.)
---
**(c) What is the probability of obtaining \( x = 15 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.12) \)?**
\( P(\hat{p} \leq 0.12) = \) [ ] (Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91e372cb-e18f-47dd-a904-4f86460a4ddf%2F66239a7d-7013-4951-a448-6f67d13c466f%2F4bw3up_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a simple random sample of size \( n = 125 \) is obtained from a population whose size is \( N = 25,000 \) and whose population proportion with a specified characteristic is \( p = 0.2 \).
[Click here to view the standard normal distribution table (page 1).]
[Click here to view the standard normal distribution table (page 2).]
---
**(a) Describe the sampling distribution of \( \hat{p} \).**
Choose the phrase that best describes the shape of the sampling distribution below.
- A. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).
- B. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).
- C. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).
- D. Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).
**Determine the mean of the sampling distribution of \( \hat{p} \).**
\( \mu_{\hat{p}} = 0.2 \) (Round to one decimal place as needed.)
**Determine the standard deviation of the sampling distribution of \( \hat{p} \).**
\( \sigma_{\hat{p}} = 0.035777 \) (Round to six decimal places as needed.)
---
**(b) What is the probability of obtaining \( x = 30 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.24) \)?**
\( P(\hat{p} \geq 0.24) = 0.1318 \) (Round to four decimal places as needed.)
---
**(c) What is the probability of obtaining \( x = 15 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.12) \)?**
\( P(\hat{p} \leq 0.12) = \) [ ] (Round to four decimal places as needed.)
Expert Solution
Step 1
Given
n=125
p=0.2
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