Algebra 2
Statistics Notes #6: The Normal Distribution
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MAFS.912.S-ID.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. A normal distribution is one of the most-used types of data distributions. These distributions are _______ - shaped and ____________________.
I. Look at the normal curves to the right. They have the same mean.
a) What is the mean of both distributions? How do you know that this is their mean?
b) On a normal curve, the point where the curve changes direction is called its inflection point.
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c) Between µ − σ? Between µ + σ?
d) Between µ − 2σ? Between µ+2 σ?
e) Between µ − 3σ? Between µ + 3σ?
f) Between µ − 2σ and µ − 3σ?
g) Above average?
2. Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches. If one woman from college is chosen randomly, find the following: a) The probability that she is taller than 65 in?
b) The probability that she is shorter than 65 in? c) The probability that she is between 62.5 and 67.5 in?
d) The probability that she is between 60 and 70 in?
e) The probability that she is between 57.5 and 72.5 in?
f) The probability that she is between 67.5 and 70 in?
g) The probability that she is below average in height?
3. The IQ scores of human beings are believed to be normally distributed with a mean of 100 and a standard deviation of 15. a) Sketch and label a normal curve to show the empirical rule for this question.
b) Estimate the range of IQ scores centered about the mean in which about 68% of people lie.
c) Estimate the range of IQ scores centered about the mean in which about 95% of people lie.
d) Estimate the range of IQ scores centered about
iv)Taking the middle value for each birth weight category calculate the mean birth weight and standard deviation, across all singleton live babies. For the category of "999g and under" use 750g as the "middle value" for this category. For the category "5000 or over" use 5250 as the middle value. Calculate the mean birth weight and standard deviation for multiple live babies. Explain the method you used giving formulae. (5 marks)
The first thing that was decided upon was to find the Mean, Median, and Mode. Using a calculator they were able to obtain the exact numbers.
...will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean. The Empirical Rule is used in statistics for showing final outcomes. After a standard deviation is found, and before exact data can be collected, this rule can be used as an estimate to the outcome of the new data. This probability can be used for gathering data that may be time consuming, or even impossible to found. When the mean equals the median and the values cluster around the mean and median, producing a bell-shaped distribution, then we can use the empirical rule to examine the variability. In this bell-shaped data set, we can calculate the mean and the standard deviation. The mean means the average value of the set of data. The standard deviation means the average scatter around the mean.
Collected data were subjected to analysis of variance using the SAS (9.1, SAS institute, 2004) statistical software package. Statistical assessments of differences between mean values were performed by the LSD test at P = 0.05.
Intelligent Quotient, or IQ score, is a measure of mental ability. It plays a major role in how individuals’ lives play out. It can be accredited for everything from personality to interests to occupation. The main debate when it comes to the subject of IQ is how a person’s score is influenced by environment and heredity. There are many theories on the matter. Some state that either heredity or environment exclusively determines IQ. Others believe that a person’s score is a result of the two. In this paper, we will analyze all of these theories and prove that while heredity plays a much greater role, they both have a very notable influence.
There are approximately 350 PDA Waiver consumers that receive services through my agency. I am going to do a random sample of the consumers that have been receiving services for more than one month. I will randomly choose 75 names from the list of PDA Waiver consumers that have been receiving services for at least one month.
There were 24 males and 24 females. These college students were divided into three groups and were interviewed with a three degree distance. Each group had the same number of student and had the same proportion of males and females. Each group were asked different tasks. Group one had to disclose something about themselves in a tape recorder while the experimenter was not in the room. On second group, the subject had to self-disclose with the experimenter in the room, however there were no eye contact between the experimenter and the subject. The third group needed to self-disclose and the experimenter did provide eye contact with the subject. On all three groups, the experimenter did not self- disclose anything about himself. The independent variable for experiment one was the absence, presence and continuous of eye contact between the experimenter and the subject. The dependent variable was the time spent for the subject to self-disclose and the duration of the
A researcher determines that 42.7% of all downtown office buildings have ventilation problems. Is this a statistic or a parameter; explain your answer.
In spite of the fact that intelligence quotient tests have been around for decades, many professionals are attempting to determine the factors and causes behind aptitude. Several options exist to explain or disprove the reasons why some attain above average intellect, while others manage varying degrees less. Some of these alternatives, along with arguments in the general and human intelligence topics, will be found inside the following pages of discussion.
...ferred because it produces meaningful information about each data point and where it falls within its normal distribution, plus provides a crude indicator of outliers. (Ben Etzkorn 2011).
The extent to which a distribution of values deviates from symmetry around the mean is the skewness. A value of zero means the distribution is symmetric, while a positive skewness indicates a greater number of smaller values, and a negative value indicates a greater number of larger values (Grad pad, 2013). Values for acceptability for psychometric purposes (+/-1 to +/-2) are the same as with kurtosis.
Based on the total means, the values of A and B were computed from the total means and standard deviations from each trait group.
After randomly choose the sample group. The 60 students will then be randomly assigned to 2 groups...
Statistics contains the development of procedures and tests that are used to describe the variability characteristic in data, the odds of certain outcomes, and the fault and doubt related with those outcomes. Some statistics are influenced, some are based on beliefs, and some are false.
Researchers, professionals and others use statistics to prove their claims or findings. Even though statistics are not an absolute fact because the conclusion is mostly drawn from a sample group – representative of a specific population subjected to the research, it is commonly used as the basis of decision making or alternating choices in daily living, studies, works, scientific research, politics and other planning. The inventor of a documentary film called “An inconvenient truth”, Mr. Al Gore, for instance, in his campaign to educate people about the climate change, used statistics to alert people that everyone on earth is polluting the environment and should participate in solving the problem. He collected data from many different countries with an in...