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MATLAB: An Introduction with Applications
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![For Problemns 1-4: The table at right shows
the probability of the number of students with
"Mathitus anmong 4 randomly selected students.
P(x)
0-
0.20
1
0.40
0.25
3
0.10
4
0.05
3. What is the standard deviation (to nearest 0.1) of the number of students with Mathitus? [Show
all of your work with a table.]
4. What is the maximum usual value of the number of students with Mathitus? Would 3 students
with Mathitus among 4 randomly selected students be considered significantly high? [Note that
within two standard deviations of the mean is considered usual or non-significant.]](https://content.bartleby.com/qna-images/question/ba6262a5-d997-4fde-9cea-b71e30254a96/291360d0-d657-4d09-a444-f0fe9b5a9f98/5ul9yyt_thumbnail.jpeg)
Transcribed Image Text:For Problemns 1-4: The table at right shows
the probability of the number of students with
"Mathitus anmong 4 randomly selected students.
P(x)
0-
0.20
1
0.40
0.25
3
0.10
4
0.05
3. What is the standard deviation (to nearest 0.1) of the number of students with Mathitus? [Show
all of your work with a table.]
4. What is the maximum usual value of the number of students with Mathitus? Would 3 students
with Mathitus among 4 randomly selected students be considered significantly high? [Note that
within two standard deviations of the mean is considered usual or non-significant.]
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- A population has a standard deviation ? of 25 units. (Give your answers correct to two decimal places.) (a) Find the standard error for the mean if n = 30.(b) Find the standard error for the mean if n = 46.(c) Find the standard error for the mean if n = 71.arrow_forwardSuppose you are working with a data set that is normally distributed, with a mean of 250 and a standard deviation of 46. Determine the value of x from the following information. (a) 70% of the values are greater than x. (b) x is less than 16% of the values. (c) 22% of the values are less than x. (d) x is greater than 55% of the values.arrow_forwardAndrew 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 over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. 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. What is the probability (assuming that past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 10%? What is the probability that the mean return will be less than 5%?arrow_forward
- Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is Skewness = 3 (mean-median)/standard deviation. The value of this measure generally lies between -3 and +3. The closer the value lies to -3, the more the distribution is skewed left. The closer the value lies to +3, the more the distribution is skewed right. A value close to 0 indicates a symmetric distribution. Find the coefficient of skewness of the following distributions and comment on the skewness. Mean = 100, median = 100, standard deviation = 15arrow_forwardA researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 51.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people. (b)Find the standard deviation of p. (c)Compute an approximation for P≥p0.515, which is the probability that there will be 51.5% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.arrow_forwardKarl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is Skewness = 3 (mean-median)/standard deviation. The value of this measure generally lies between -3 and +3. The closer the value lies to -3, the more the distribution is skewed left. The closer the value lies to +3, the more the distribution is skewed right. A value close to 0 indicates a symmetric distribution. Find the coefficient of skewness of the following distributions and comment on the skewness. Compute the coefficient of skewness for this data (See photo): The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geyser in Calistoga, California.arrow_forward
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