To change from a close interval to a normal interval, the command "Change interval, march" is used. This instructs the squad to adjust their spacing to the standard distance between individuals. Upon receiving the command, each member of the squad will move to the designated position to maintain proper alignment and distance.
Normal Distribution is a key to Statistics. It is a limiting case of Binomial and Poisson distribution also. Central limit theorem converts random variable to normal random variable. Also central limit theorem tells us whether data items from a sample space lies in an interval at 1%, 5%, 10% siginificane level.
It depends whether or not the observations are independent and on the distribution of the variable that is being measured or the sample size. You cannot simply assume that the observations are independent and that the distribution is Gaussian (Normal).
Standard deviation is a measure of the dispersion of the data. When the standard deviation is greater than the mean, a coefficient of variation is greater than one. See: http://en.wikipedia.org/wiki/Coefficient_of_variation If you assume the data is normally distributed, then the lower limit of the interval of the mean +/- one standard deviation (68% confidence interval) will be a negative value. If it is not realistic to have negative values, then the assumption of a normal distribution may be in error and you should consider other distributions. Common distributions with no negative values are gamma, log normal and exponential.
Short answer, complex. I presume you're in a basic stats class so your dealing with something like a normal distribution however (or something else very standard). You can think of it this way... A confidence interval re-scales margin of likely error into a range. This allows you to say something along the lines, "I can say with 95% confidence that the mean/variance/whatever lies within whatever and whatever" because you're taking into account the likely error in your prediction (as long as the distribution is what you think it is and all stats are what you think they are). This is because, if you know all of the things I listed with absolute certainty, you are able to accurately predict how erroneous your prediction will be. It's because central limit theory allow you to assume statistically relevance of the sample, even given an infinite population of data. The main idea of a confidence interval is to create and interval which is likely to include a population parameter within that interval. Sample data is the source of the confidence interval. You will use your best point estimate which may be the sample mean or the sample proportion, depending on what the problems asks for. Then, you add or subtract the margin of error to get the actual interval. To compute the margin of error, you will always use or calculate a standard deviation. An example is the confidence interval for the mean. The best point estimate for the population mean is the sample mean according to the central limit theorem. So you add and subtract the margin of error from that. Now the margin of error in the case of confidence intervals for the mean is za/2 x Sigma/ Square root of n where a is 1- confidence level. For example, confidence level is 95%, a=1-.95=.05 and a/2 is .025. So we use the z score the corresponds to .025 in each tail of the standard normal distribution. This will be. z=1.96. So if Sigma is the population standard deviation, than Sigma/square root of n is called the standard error of the mean. It is the standard deviation of the sampling distribution of all the means for every possible sample of size n take from your population ( Central limit theorem again). So our confidence interval is the sample mean + or - 1.96 ( Population Standard deviation/ square root of sample size. If we don't know the population standard deviation, we use the sample one but then we must use a t distribution instead of a z one. So we replace the z score with an appropriate t score. In the case of confidence interval for a proportion, we compute and use the standard deviation of the distribution of all the proportions. Once again, the central limit theorem tells us to do this. I will post a link for that theorem. It is the key to really understanding what is going on here!
In the simplest setting, a continuous random variable is one that can assume any value on some interval of the real numbers. For example, a uniform random variable is often defined on the unit interval [0,1], which means that this random variable could assume any value between 0 and 1, including 0 and 1. Some possibilities would be 1/3, 0.3214, pi/4, e/5, and so on ... in other words, any of the numbers in that interval. As another example, a normal random variable can assume any value between -infinity and +infinity (another interval). Most of these values would be extremely unlikely to occur but they would be possible. The random variable could assume values of 3, -10000, pi, 1000*pi, e*e, ... any possible value in the real numbers. It is also possible to define continue random variables that assume values on the entire (x,y) plane, or just on the circumference of a circle, or anywhere that you can imagine that is essentially equivalent (in some sense) to pieces of a real line.
normal interval, MARCH
At close interval, MARCH!
Double Interval, MARCH
To change from close interval to normal interval, the command used is "Dress Right, Dress." This command directs the squad to align themselves at normal intervals, ensuring that each member has enough space between them for proper formation. Following this command, the squad will adjust their positions to achieve the desired spacing.
When a squad is changing intervals, the command used to obtain a normal interval is "Dress Right, Dress." To achieve a close interval, the command is "Close Interval, Dress Right, Dress." These commands ensure proper formation and spacing among squad members during movements.
When a squad is changing from normal interval to close interval, the command used is "Close intervals, dress right." This command prompts the squad members to move closer together, ensuring they maintain proper alignment and spacing as they adjust to the new formation. The command helps facilitate a more compact formation while maintaining order and discipline.
When a squad is changing intervals, the command used to obtain a normal interval is "Dress Right, Dress." This command prompts the members of the squad to align themselves in a straight line at equal distances from one another, ensuring proper spacing. Following this, the command "Ready, Front" is typically given to return the squad to the position of attention.
Normal interval, close interval, and double interval
When a squad is changing from close interval to normal interval, the command used is "Open ranks, march." This command instructs the squad to adjust their spacing to achieve the proper distance between individuals, ensuring they maintain a normal interval. The movement typically involves stepping to the side to create the required space while remaining aligned with the squad.
Normal interval, close interval, and double interval
The command used to obtain a normal interval from a close interval in a squad formation is "Dress Right, Dress." This command directs the squad members to adjust their positions to ensure they are evenly spaced and aligned, maintaining a proper distance from each other. Following this command, members typically take a step to the right and align themselves to achieve the desired spacing.
Normal Interval