How do I change the following post comparing sample mean to comparing values? Th

Question

How do I change the following post comparing sample mean to comparing values?

The original question is :

Countless phenomena follow a normal distribution and therefor it is perhaps the most important of the theoretical distributions applied to continuous variables. The normal distribution is important to statistical work because most hypothesis tests that are used assume that the random variable being considered has an underlying normal distribution. Using your topic of interest what phenomena might you be interested in measuring as it applies to normal distribution? Be sure you show me you understand not only the principle of the distribution (and subsequent curve) but also how mean and standard deviation might influence or be significant in your proposed area of study.

My answer was this below but needs to be corrected to answer the original question.

To answer the question, we first need to establish that a graph of the normal distribution depends on two factors: the mean and the standard deviation. The mean of the distribution determines the location of the center of the graph, and the standard deviation defines the height and width of the chart. When the standard deviation is large, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow. All normal distributions look like a symmetric, bell-shaped curve.(Lock, 2013, p. 324) It is often the case with medical data or public health data if we were using a histogram of a continuous variable obtained from a single measurement on different subjects we would clearly see that "bell-shaped" distribution or "normal distribution." Using a public health example, that is of particular importance to me in my work on health equity, is the birth weight of children born in the state of Oregon between 2013-2015. We can presume that if we were able to look at the entire population of newborn babies, then the distribution of birth weight would have exactly the “normal distribution” shape. Using formulas, we can describe a “normal distribution” using the parameters and . Then, represents the population mean, or center of the distribution, and the population standard deviation. Populations with small values of the standard deviation have a distribution concentrated close to the center ; those with large standard deviation have a distribution wider and more spread in the axis. (Lock, 2013, p. 326) A particular property of a “normal distribution” is that exactly 95% of the distribution lies between - (1.96 x ) and + (1.96 x ) Changing the multiplier 1.96 to 2.58, exactly 99% of the Normal distribution lies in the corresponding interval. If we were to chart our sample birth weight data we could see that appears “normally distributed,” to calculate a reference range. We have already mentioned that about 95% of the observations (from a Normal distribution) lie within ±1.96 SDs of the mean. So a reference range for our sample of Oregon babies would be 2.31kg to 4.47kg. A baby's weight at birth has many associations such as with mortality risk during the first year; with developmental problems in childhood and with the risk of many diseases in adulthood. Over many years, and millions of births, the World Health Organization has come up with a normal birth weight range for newborn babies. These ranges represent results than are acceptable in newborn babies and cover the middle 80% of the population distribution, for example, 10th to 90th centiles. Low birth weight babies are usually defined (by the WHO) as weighing less than 2,500g (the 10th centile) regardless of gestational age, and large birth weight babies are defined as weighing above 4,000kg (the 90th centile). Hence the normal birth weight range is around 2.5kg to 4kg. In the case of our Oregon babies data, the 10th to 90th centile range was similar, 2.75 to 4.03kg.

Explanation / Answer

we first need to establish that a graph of the normal distribution depends on two parameters the mean and the standard deviation. The mean of the distribution determines the location of the center of the graph, and the standard deviation defines the kurtosis and skewness of the data. When the curve is short and wide then its platykurtic when the curve is tall and narrow it is leptokurtic .All normal distributions look like a symmetric, bell-shaped curve, using central limit theorem we have the result most of the distributions follows normal distribution when n is large.Basically we have large number of population in dealing with any natural phenomenon thus using Central limit theorem it follows normal distrubtion.It is often the case with medical data or public health data if we were using a histogram of a continuous variable obtained from a single measurement on different subjects we would clearly see that "bell-shaped" distribution or "normal distribution." Using a public health example, that is of particular importance to me in my work on health equity, is the birth weight of children born in the state of Oregon between 2013-2015. We can presume that if we were able to look at the entire population of newborn babies, then the distribution of birth weight would have exactly the “normal distribution” shape. Using formulas, we can describe a “normal distribution” using the parameters and . Then, represents the population mean, or center of the distribution, and the population standard deviation. Populations with small values of the standard deviation have a distribution concentrated close to the center ; those with large standard deviation have a distribution wider and more spread in the axis. (Lock, 2013, p. 326).A particular property of a “normal distribution” is that exactly 95% of the data points lies between - (1.96 x ) and + (1.96 x ) Changing the multiplier 1.96 to 2.58, exactly 99% of data points lies in the corresponding interval. If we were to chart our sample birth weight data we could see that appears “normally distributed,” to calculate a reference range. We have already mentioned that about 95% of the observations (from a Normal distribution) lie within ±1.96 SDs of the mean. So a reference range for our sample of Oregon babies would be 2.31kg to 4.47kg. A baby's weight at birth has many associations such as with mortality risk during the first year; with developmental problems in childhood and with the risk of many diseases in adulthood. Over many years, and millions of births, the World Health Organization has come up with a normal birth weight range for newborn babies. These ranges represent results than are acceptable in newborn babies and cover the middle 80% of the population distribution, for example, 10th to 90th centiles. Low birth weight babies are usually defined (by the WHO) as weighing less than 2,500g (the 10th centile) regardless of gestational age, and large birth weight babies are defined as weighing above 4,000kg (the 90th centile). Hence the normal birth weight range is around 2.5kg to 4kg. In the case of our Oregon babies data, the 10th to 90th centile range was similar, 2.75 to 4.03kg.

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