4. A publisher believes that the length of time per day that adults spend reading newspapers has a mean of 8.5 minutes and a standard deviation of 1.25 minutes. A random sample of 40 adults is chosen. Mos.s J=1,25 n=40 A. The mean and standard error of the sample mean x are H = M=8,5 い25 =1976423538 B. Find the approximate probability that the sample mean is between 8.8 and 9.3. In other words find P(8.8 < x < 9.3) = z==-M - (8.8-8.5)-1.517 p/G8く5く 9.3
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Can I have two positive numbers with a
![### Statistical Analysis of Time Spent Reading Newspapers
**Scenario:**
A publisher believes that the length of time per day that adults spend reading newspapers has a mean of 8.5 minutes and a standard deviation of 1.25 minutes. A random sample of 40 adults is selected to further analyze the data.
#### Part A: Mean and Standard Error of the Sample Mean
- **Mean of the Sample Mean (\(\mu_{\bar{x}}\))**: The mean of the sample mean is given as 8.5.
\[
\mu_{\bar{x}} = 8.5
\]
- **Standard Error of the Sample Mean (\(\sigma_{\bar{x}}\))**: The standard error is calculated using the formula:
\[
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
\]
Substituting the given values:
\[
\sigma_{\bar{x}} = \frac{1.25}{\sqrt{40}} = 0.1976423538
\]
#### Part B: Probability Calculation
- **Objective**: Find the approximate probability that the sample mean (\(\bar{x}\)) is between 8.8 and 9.3 minutes.
\[
P(8.8 < \bar{x} < 9.3)
\]
- **Standardized Z-scores Calculation**: Use the Z-score formula for each boundary.
\[
Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
- **For 8.8 minutes**:
\[
Z = \frac{8.8 - 8.5}{1.25 / \sqrt{40}} = \frac{0.3}{0.1976423538} = 1.517
\]
- **For 9.3 minutes**:
\[
Z = \frac{9.3 - 8.5}{1.25 / \sqrt{40}} = \frac{0.8}{0.1976423538} = 4.047
\]
### Graphs/Diagrams Explanation
- There are no graphs or diagrams included in the image. Calculations are solely based on statistical formulas and standard normal distribution properties.
This page explains how to determine the mean, standard error of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bc805eb-60ed-457b-ab8e-02c516698c74%2F9c360fdd-4bc8-4739-a65d-8f8f9bcf5d9e%2Fgt9t4kl_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
