**Problem:** After doubling all of the scores, the mean was found to be 28 and the standard deviation was 4. What were the values for the mean and standard deviation (SD) before the change? Explain.**Solution:** To find the original mean and standard deviation before the scores were doubled, we can use the properties of mean and standard deviation with respect to scaling:1. **Mean:** - If all scores are doubled, the mean of the scores is also doubled. - Thus, if the doubled mean is 28, the original mean ($\mu$) is: \[ \mu = \frac{28}{2} = 14 \]2. **Standard Deviation:** - The standard deviation also scales linearly with multiplication. - If the doubled standard deviation is 4, the original standard deviation ($\sigma$) is: \[ \sigma = \frac{4}{2} = 2 \]Therefore, before doubling, the mean of the scores was 14 and the standard deviation was 2.

Let's denote the original mean as and the original standard deviation as .After doubling all of the…

Answered: 2) After doubling all of the scores,…

2) After doubling all of the scores, the mean was found to be 28 and the standard deviation was 4. What were the values for the mean and SD before the change? Explain

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: A researcher studying stress is interested in the blood pressure measurements of chief executive…

A: From the given information we have The null and alternative hypothesis are H0 : µ = 132H1: µ >…

Q: What is the corresponding Z- score, mean is 110, standard deviation is 8 and x is 90

A: In question, We'll find the Z - score for mean 110, standard deviation 8 and x = 90. The solution is…

Q: u and your friend have recently taken two different standardized mathematics exams. You scored 92 on…

A: The mean = 100The standard deviation = 10

Q: what percent of values fall between 5.25 and 8.75 if the mean =9 and standard deviation =2.36

A: Answer: From the given data, Mean (μ) = 9 Standard deviation (σ) = 2.36 X follows normal…

Q: 3. The number of miles traveled per gallon of gasoline for a certain car has a mean of 25 and a…

A: Given that Mean=25 Standard deviation =2 Sample size n=20

Q: You have a dataset with a mean of 2, median of 3 and variance of 9. What is the skewness?

A: Given that Mean = 2 , Median = 3 , Variance = 9

Q: how do you calculate the mean and standard deviation without a calculator ?

A: In this question we have to tell that how to find the Mean and Standard deviation without using the…

Q: If the main level of snowfall for Boston Massachusetts is 44 inches per year and the standard…

Q: You have a dataset with a mean of 50 and a standard deviation of 5. What is the coefficient of…

A: From the provided information, Mean (x̄) = 50 Standard deviation (s) = 5

Q: The mean weight of babies born in Central hospital last year was 7.2 pounds. Suppose the standard…

Q: Explain with an example of the distribution of values around the mean by using general rules.…

A: We have to find given distribution.

Q: One year, many college-bound high school seniors in the US took the SAT. For the verbal portion of…

A: According to the given information in this question We need to find the percentage of students would…

Q: You want to know the percentage of financial services companies that earned revenue less than 8181…

A: The objective of this question is to find the percentage of financial services companies that earned…

Q: Would you be able to help with Standard Deviation along with the range, mean, mode, and median?

A: Measures of variability:The measure of variability or the measures of dispersion can be measured…

Q: he average height for a man in California was 177 cm in 2021. If height follows a normal…

A: given data, normal distribution, μ=177σ=10p(180<X<190)=?

Q: is 80 a suspect outlier

A: Here given, One indicator of an outlier is that an observation is more than 2.5 standard deviations…

Q: The results of a common standardized test used in psychology research is designed so that the…

A: The standard normal value helps to understand the number of deviation of observations from the mean.…

Q: What is the mean absolute deviation of 5 scores if their deviation from the mean are 6, -5, 4, 3 and…

Q: How do I figure out snowfall is 98 inches per year and the standard deviation is 25 inches. What…

A: We have to find percentage of the time does the city receive less than 125 inches.

Q: Consider a value to be significantly low if its z score less than or equal to -2 or consider a value…

A: Here, mean is 19.5 and standard deviation is 4.6.

Q: Explain an important difference between the standard deviation and the mean.

Q: A commonly used standardized test in psychology research is designed so that the mean score of all…

A: From the provided information, Mean (µ) = 140 Standard deviation (σ) = 20 X~N (140, 20) Here X be a…

Q: Assume a new measure of Intelligence Quotient (or IQ) has been developed. The mean IQ for the…

A: The standard deviation is defined how much deviation from the mean is called standard deviation.

Q: Mean is 235, standard deviation is 52, what is the percentile of a raw score of 28

A: Mean Standard deviation

Q: what percent of values fall between 5.25 and 8.75 if the mean =8 and standard deviation =1.89

A: Mean=8 Standard deviations=1.89

Q: The scores on a test are normally distributed, with a mean of 82 and standard deviation of 5. What…

A: Let X be the random variable from normal distribution with mean (μ) = 82 and standard deviation (σ)…

Q: ASK YOUR TEACHER Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous…

Q: The weights of men are normally with a mean of 172 pounds and a standard deviation of 29 pounds.…

A: Let X be the random variable from normal distribution with mean (μ) = 172 and standard deviation (σ)…

Q: what percent of values fall between 5.25 and 8.75 if the mean =7 and standard deviation =1.75

A: Mean=7 Standard deviations=1.75

Q: basketball coach kept stats for his team in free throw percentage and steals (among others). At the…

A: Solution To find in which category did Erin do better compared with her team we will use z score.

Q: I don't understand how to use the given information to answer the questions about the mean and…

A: Given probability distribution…

Q: in how you determined your findings. How many children scored lower than Emily? How many children…

A: The standard normal variate of the normal distribution is continuous and follows that z~N(0,1). The…

Q: what percent of values fall between 5.25 and 8.75 if the mean =5 and standard deviation =1.86

A: Answer: From the given data, Mean (μ) = 5 Standard deviation (σ) = 1.86 X follows normal…

Q: You have a data set with mean = 40 and standard deviation = 3. What can you say about the percentage…

A: Given μ=mean=40, sd=σ=3 P(32<X<40)= ? Note: this probability value calculated from standard…

Q: tter measurement of the spread of data than simply taking the sum of the deviations of each x value…

A: Spread of the data means how far the values are there from the mean.

Q: Many students did an exam, the mean was 15 and the standard deviation was 32 The highest mark was…

A: Given Mean μ=15, standard deviation σ=32 X=103

Q: Explain what would happen if Person A scored lower than the mean of 70. Give an example exam score…

A: To compare the performance of Person A and Person B on their respective exams with their classmates,…

Q: You are going to convert raw scores to z scores. The z scores are -2, -1, 0, +1, +2. The raw scores…

A: We have given that X~N( mu, sigma^2) Z-score =(x- mu)/sigma

Question

**Problem:**
After doubling all of the scores, the mean was found to be 28 and the standard deviation was 4. What were the values for the mean and standard deviation (SD) before the change? Explain.

**Solution:**
To find the original mean and standard deviation before the scores were doubled, we can use the properties of mean and standard deviation with respect to scaling:

1. **Mean:**
- If all scores are doubled, the mean of the scores is also doubled.
- Thus, if the doubled mean is 28, the original mean ($\mu$) is:
\[ \mu = \frac{28}{2} = 14 \]

2. **Standard Deviation:**
- The standard deviation also scales linearly with multiplication.
- If the doubled standard deviation is 4, the original standard deviation ($\sigma$) is:
\[ \sigma = \frac{4}{2} = 2 \]

Therefore, before doubling, the mean of the scores was 14 and the standard deviation was 2.

Expert Solution

Step 1: Given

Let's denote the original mean as $mu$ and the original standard deviation as $sigma$ .

After doubling all of the scores, the new mean ( $mu apostrophe$ ) and new standard deviation ( $sigma apostrophe$ ) were found to be 28 and 4, respectively.

Step by step

Solved in 3 steps with 10 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

please help me answer this all. if i divided it it just became hard explain it. please i give a thumbs up. answer this.
Why would you use mean absolute deviation as opposed to the mean average?
State two ways the standard deviation differs from the average deviation.
According to the U.S. Census, the average adult woman is the United States is 65 inches tall and the standard deviation is 3 inches. If Zsike is 67 inches tall, what is her z-score?
If the mean snowfall for Ottawa Ontario Canada is 98 inches per year and the standard deviation is 25 inches what percentage of the time does Ottawa receive less than 125 inches of snow?
I need help solving this statistics problem.
What if a professor returned an assignment to you and your assignment score is 85 had a standard deviation of 8 and the professor told you that the class mean was 75. What would be your percentile.
Answer according to Swikness theorm. Thank you • Illustration: The mean and standard deviation of a set of 100 observations were 40 and 5 respectively by a computer which by mistake took the value 50 in worked out as place of 40 for one observation. Find the correct mean and variance.
You scored a 85 on a stats test with a mean of 70 and a standard deviation of 7. Youalso score a 90 on a Bio test with a mean of 80 and a standard deviation of 8. Inwhich test did you score better, relative to the other test takers? What measure areyou using to answer this question?
After calculating the mean and standard deviation, how do we interpret the result, and when a variable look strange?
Mario's weekly poker winnings have a mean of $353 and a standard deviation of $67. Last week he won $185. How many standard deviations from the mean is that?
What does the standard deviation tell you about a set of data?