**Question 11 of 23****STATE:** Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that from 1966 to 2015, the annual returns on the S&P 500 had a mean of 11.0% and a standard deviation of 17.0%.**PLAN:** The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. We can use the Central Limit Theorem to make an inference.**SOLVE:** What is the probability, $p_1$, assuming that the past pattern of variation continues, that the mean annual return on common stocks over the next 40 years will exceed 10%? (Enter your answer rounded to two decimal places.)\[ p_1 = \]---There are no graphs or diagrams in the image, only text related to a statistical problem concerning investment returns. The image presents a statistics exercise on calculating probabilities. Here’s the transcription suitable for an educational website:---**Exercise: Probability Calculation**$ p_1 = \_\_\_\_\_\_\_\_\_ $**Question:** What is the probability, $ p_2 $, that the mean return will be less than 5%? (Enter your answer rounded to two decimal places.)$ p_2 = \_\_\_\_\_\_\_\_\_ $**CONCLUDE:** Select the correct conclusion based on the results.---**Additional Information:**- The source of the question is: Moore, *The Basic Practice of Statistics, 8e*.- Publisher: W.H. Freeman.This exercise is designed to enhance skills in probability theory and statistical analysis.

Name: **Question 11 of 23****STATE:** Andrew plans to retire in 40 years. H
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Description: **Question 11 of 23****STATE:** Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that from 1966 to 2015, the annual returns on the S&P 500 had a mea

The mean annual return for common stocks for 40 years will follow normal distribution with…

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Statistics

STATE: Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that from 1966 to 2015, the annual returns on S&P 500 had mean 11.0% and standard deviation 17.0%. PLAN: The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. We can use the Central Limit Theorem to make an inference. SOLVE: What is the probability, p1, assuming that the past pattern of variation continues, that the mean annual return on common stocks over the next 40 years will exceed 10% ? (Enter your answer rounded to two decimal places.)

STATE: Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that from 1966 to 2015, the annual returns on S&P 500 had mean 11.0% and standard deviation 17.0%. PLAN: The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. We can use the Central Limit Theorem to make an inference. SOLVE: What is the probability, p1, assuming that the past pattern of variation continues, that the mean annual return on common stocks over the next 40 years will exceed 10% ? (Enter your answer rounded to two decimal places.)

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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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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The image presents a statistics exercise on calculating probabilities. Here’s the transcription suitable for an educational website:

---

**Exercise: Probability Calculation**

$ p_1 = \_\_\_\_\_\_\_\_\_ $

**Question:** What is the probability, $ p_2 $, that the mean return will be less than 5%? (Enter your answer rounded to two decimal places.)

$ p_2 = \_\_\_\_\_\_\_\_\_ $

**CONCLUDE:** Select the correct conclusion based on the results.

---

**Additional Information:**
- The source of the question is: Moore, *The Basic Practice of Statistics, 8e*.
- Publisher: W.H. Freeman.

This exercise is designed to enhance skills in probability theory and statistical analysis.

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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 221 numerical entries from the file and r = 50 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i) Test the claim that p is less than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.301; H₁: p = 0.301 Ho: P 0.301 Ho: P = 0.301; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the…
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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 220 numerical entries from the file and r = 49 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. A) What is the value of the sample test statistic? (Round your answer to two decimal places.)B) Find the P-value of the test statistic. (Round your answer to four decimal places.)
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