Question

Consider what you have learned about the shape normal distribution and specifically about the Empirical Rule. Please compare and contrast Roger’s Innovation Adoption Curve with what you have learned. Be as specific as possible in your explanations making reference to Roger’s Innovation Adoption Curve, the normal distribution, and the Empirical Rule .

Answer 1

Shape Normal Distribution:

A normal distribution is a true symmetric distribution of observed values. When a histogram is constructed on values that are normally distributed, the shape of columns form a symmetrical bell shape. This is why this distribution is also known as a 'normal curve' or 'bell curve'.

Emperical Rule:

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

The empirical rule is often used in statistics for forecasting final outcomes. After calculating the standard deviation and before collecting exact data, this rule can be used as a rough estimate of the outcome of the impending data. This probability can be used in the interim since gathering appropriate data may be time-consuming or even impossible. The empirical rule is also used as a rough way to test a distribution's "normality". If too many data points fall outside the three standard deviation boundaries, this suggests that the distribution is not normal.

Roger’s Innovation Adoption Curve :

The innovation adoption curve classifies the entry of users into various categories, based on their willingness to accept new technology or an idea. It is useful in breaking down or segregating consumers into five different segments or categories such as innovators, early adopters, early majority, late majority, and laggards.

The innovation adoption curve follows a bell-shaped curve, which can be divided into five different categories. Let's discuss each one of them in detail. Usually, the innovators are the first ones to adopt the new idea or the technology. They consist of a small percentage of the population, almost 2.5 per cent. They are the ones who are young and willing to take risks about the new technology.

The next ones are early adopters. Early adopters consist of almost 13.5 per cent. One characteristic which differentiates this group from the others is that they have a high degree of leadership or influencing power. They are also young individuals who are willing to take that extra risk.

The third category of individuals who adopt an innovation is Early Majority (34%). The only difference is that here the time of adoption is slightly longer, but the percentage is higher than innovators and early adopters. They have an above-average social status, and accept change more quickly than the average.

The fourth category of is Late Majority (34%). The individuals in this category take a lot of time to adopt new technology. They are the ones who will do research because they are sceptical of innovation. They adopt the new technology because of peer pressure.

Laggards is the fifty category of individuals who adopt an innovation. They are reluctant to any change. By the time laggards adopt the new technology it might have already become obsolete. They are fixated on past methods or technology for their daily usage.

So we can say that in shape normal distribution there are no parts where Roger's Adoption Curve has five parts. And in case of Empirical Rule there are 3 parts. This the main difference among three.