Suppose a simple random sample of size n= 39 is obtained from a population with p = 62 and o = 19. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x< 65.2). (c) Assuming the normal model can be used, determine P(x2 63.2). Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2). (a) What must be true regarding the distribution of the population? O A. The population must be normally distributed. O B. The population must be normally distributed and the sample size must be large. Oc. Since the sample size is large enough, the population distribution does not need to be normal. O D. There are no requirements on the shape of the distribution of the population. Assuming the normal model can be used, describe the sampling distribution x. 39 O A. Approximately normal, with µ; = 62 and o; = V19 19 O B. Approximately normal, with p, = 62 and o; = V39 OC. Approximately normal, with p; = 62 and o; = 19 (b) P(x < 65.2) = (Round to four decimal places as needed.) (c) P(x2 63.2) = (Round to four decimal places as needed.)
Suppose a simple random sample of size n= 39 is obtained from a population with p = 62 and o = 19. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x< 65.2). (c) Assuming the normal model can be used, determine P(x2 63.2). Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2). (a) What must be true regarding the distribution of the population? O A. The population must be normally distributed. O B. The population must be normally distributed and the sample size must be large. Oc. Since the sample size is large enough, the population distribution does not need to be normal. O D. There are no requirements on the shape of the distribution of the population. Assuming the normal model can be used, describe the sampling distribution x. 39 O A. Approximately normal, with µ; = 62 and o; = V19 19 O B. Approximately normal, with p, = 62 and o; = V39 OC. Approximately normal, with p; = 62 and o; = 19 (b) P(x < 65.2) = (Round to four decimal places as needed.) (c) P(x2 63.2) = (Round to four decimal places as needed.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:# Standard Normal Distribution Table
## Overview
The standard normal distribution table provides the area under the standard normal curve (a bell-shaped curve), which is crucial for statistical analysis. The table helps in finding the probability that a standard normal random variable \( Z \) is less than or equal to a given value (i.e., \( P(Z \leq z) \)).
### Diagram
Each page contains a diagram of the standard normal distribution, a bell-shaped curve symmetrically centered at \( z = 0 \). The area under the curve to the left of a specific \( z \)-score represents the cumulative probability. An area shaded in light color illustrates this concept.
## Page 1
### Description
- **Z-Score Values**: Begin at \(-3.4\) and increase by \(0.1\) increments.
- **Columns**: Represent decimal increments from \( z.00 \) to \( z.09 \).
- **Table Data**: Provides cumulative probabilities for each corresponding \( z \)-score.
### Example
To find the probability \( P(Z \leq -2.5) \):
- Locate \(-2.5\) on the leftmost column.
- Align with column \( z.00 \).
- Find probability \(0.0062\).
## Page 2
### Description
- **Z-Score Values**: Begin at \(0.0\) and increase by \(0.1\) increments.
- **Same column format** as Page 1.
- **Table Data**: Provides cumulative probabilities for positive \( z \)-scores.
### Example
To find the probability \( P(Z \leq 1.3) \):
- Locate \(1.3\) on the leftmost column.
- Align with column \( z.00 \).
- Find probability \(0.9032\).
This table is essential in statistics for hypothesis testing and various calculations involving normal distribution.
![Suppose a simple random sample of size \( n = 39 \) is obtained from a population with \( \mu = 62 \) and \( \sigma = 19 \).
### Questions
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution \( \bar{x} \).
(b) Assuming the normal model can be used, determine \( P(\bar{x} < 65.2) \).
(c) Assuming the normal model can be used, determine \( P(\bar{x} \geq 63.2) \).
[Click here to view the standard normal distribution table (page 1)]
[Click here to view the standard normal distribution table (page 2)]
### Options for the Questions
**(a) What must be true regarding the distribution of the population?**
- **A.** The population must be normally distributed.
- **B.** The population must be normally distributed and the sample size must be large.
- **C.** Since the sample size is large enough, the population distribution does not need to be normal.
- **D.** There are no requirements on the shape of the distribution of the population.
**Assuming the normal model can be used, describe the sampling distribution \( \bar{x} \).**
- **A.** Approximately normal, with \( \mu_{\bar{x}} = 62 \) and \( \sigma_{\bar{x}} = \frac{39}{\sqrt{19}} \)
- **B.** Approximately normal, with \( \mu_{\bar{x}} = 62 \) and \( \sigma_{\bar{x}} = \frac{19}{\sqrt{39}} \)
- **C.** Approximately normal, with \( \mu_{\bar{x}} = 62 \) and \( \sigma_{\bar{x}} = 19 \)
### Calculations
**(b) \( P(\bar{x} < 65.2) = \) \(\square\) (Round to four decimal places as needed.)**
**(c) \( P(\bar{x} \geq 63.2) = \) \(\square\) (Round to four decimal places as needed.)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2e8082e-e138-4303-88b5-dd606869428c%2Fcc72637e-e827-4516-ad69-dfff5dedc091%2Fbx7cgm6_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a simple random sample of size \( n = 39 \) is obtained from a population with \( \mu = 62 \) and \( \sigma = 19 \).
### Questions
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution \( \bar{x} \).
(b) Assuming the normal model can be used, determine \( P(\bar{x} < 65.2) \).
(c) Assuming the normal model can be used, determine \( P(\bar{x} \geq 63.2) \).
[Click here to view the standard normal distribution table (page 1)]
[Click here to view the standard normal distribution table (page 2)]
### Options for the Questions
**(a) What must be true regarding the distribution of the population?**
- **A.** The population must be normally distributed.
- **B.** The population must be normally distributed and the sample size must be large.
- **C.** Since the sample size is large enough, the population distribution does not need to be normal.
- **D.** There are no requirements on the shape of the distribution of the population.
**Assuming the normal model can be used, describe the sampling distribution \( \bar{x} \).**
- **A.** Approximately normal, with \( \mu_{\bar{x}} = 62 \) and \( \sigma_{\bar{x}} = \frac{39}{\sqrt{19}} \)
- **B.** Approximately normal, with \( \mu_{\bar{x}} = 62 \) and \( \sigma_{\bar{x}} = \frac{19}{\sqrt{39}} \)
- **C.** Approximately normal, with \( \mu_{\bar{x}} = 62 \) and \( \sigma_{\bar{x}} = 19 \)
### Calculations
**(b) \( P(\bar{x} < 65.2) = \) \(\square\) (Round to four decimal places as needed.)**
**(c) \( P(\bar{x} \geq 63.2) = \) \(\square\) (Round to four decimal places as needed.)**
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