In each case, consider what you know about the distribution
and then explain why you would expect it to be
or not to be normally distributed.
I am really having a hard time understanding this. Any help would be great.
a. The wealth of the parents of students attending your
school
b. The values that a group of fourth-grade students
would give for the length of a segment that they
measured with a ruler
c. The SAT or ACT examination scores in mathematics
for students who were in your high school
graduation class
d. The weights of all incoming freshman students at
your school
Check my replies below, just getting to it
I am new to this website where is your reply?
You asked the same question twice, scroll down.
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a. The wealth of the parents of students attending your school
The distribution of wealth is typically not normally distributed because it is often skewed. In most societies, there is a significant wealth disparity, with a small portion of the population holding a large portion of the wealth. This creates a long right tail in the distribution, meaning that a few individuals have extremely high levels of wealth. Additionally, wealth is influenced by various factors such as inheritance, investments, and business success, which can lead to a non-normal distribution.
To understand this, you can gather data on the wealth of parents of students in your school. You can use surveys, interviews, or publicly available financial information to collect data. After collecting the data, you can plot a histogram or a box plot to examine the distribution. If the distribution is skewed, with a longer right tail and more values on the lower end of the scale, it would suggest a non-normal distribution of wealth.
b. The values that a group of fourth-grade students would give for the length of a segment that they measured with a ruler
The distribution of the length of segments measured by fourth-grade students is likely to be normally distributed. When measuring a physical quantity like length, human errors and variation in measurement are expected. These errors often follow a normal distribution, as they can be influenced by factors like perception, motor skills, and concentration levels. These errors can cancel each other out and lead to a symmetric distribution around the true value of the segment length.
To verify this, you can conduct a measurement exercise with a group of fourth-grade students, providing them with rulers and asking them to measure the length of various segments. Collect the measured values and examine their distribution using a histogram or a normal probability plot. If the distribution is approximately symmetric and bell-shaped, it would suggest a normal distribution of the measured segment lengths.
c. The SAT or ACT examination scores in mathematics for students who were in your high school graduation class
The distribution of SAT or ACT examination scores in mathematics for high school students is often approximately normally distributed. These standardized tests are designed to assess the overall ability of students in different academic areas, including mathematics. Due to the large number of students taking these exams and the random nature of test performance, the distribution of scores tends to follow a bell-shaped curve.
To confirm this, you can obtain the SAT or ACT examination scores of the students in your high school graduation class. Plotting a histogram or examining a normal probability plot for these scores can help determine if they follow a normal distribution. If the distribution is symmetric and approximately bell-shaped, it would indicate a normally distributed scores.
d. The weights of all incoming freshman students at your school
The distribution of weights of incoming freshman students is likely to be approximately normally distributed. Human body weight is influenced by various factors such as genetics, lifestyle, and diet. These factors, combined with the large number of students and the random nature of weight variation, contribute to a distribution that can be approximated by a normal curve.
To analyze this, you can collect the weights of incoming freshman students at your school. This data can be obtained through surveys, medical records, or weigh-ins during registration. Once you have the weights, you can plot a histogram or examine a normal probability plot to determine if the distribution is bell-shaped and symmetric. If the distribution closely resembles a normal curve, it would suggest a normally distributed weights of the incoming freshman students.