Question

5. Why do we want to know what the standard error of the sampling distribution equals? 6. When does a binomial distribution begin to approximate a Poisson distribution? As discussed in class, what is the main reason we need to understand the normal distribution? 7. 8. There is a pipe-making machine. On any given day it averages about 5 errors for about 10,000 feet of pipe; however, it ends to make more errors in the morning when the machine is warming up. Nevertheless, errors are still independent from each other. Just because one error was made does not change the probability that another error will be made. Could it be problematic using the Poisson distribution to calculate the probabilities of this machine to make certain number of errors? Please explain.

Answer 1

Ans 5 In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error. The standard error is a statistical term that measures the accuracy with which a sample represents a population. The smaller the standard error, the more representative the sample will be of the overall population. The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size, the larger the sample size, the smaller the standard error because the sample will approach the actual value. The standard error can include the variation between the calculated mean of the population and one which is considered known or accepted as accurate. This helps finding out the incompetencies and mistake in the sample taken from the big data.

Ans 6 The Binomial distribution can become Poisson when

• n is greater than or equals to 20
• p is less than or equals to .05
• n * p is less than 10,

where n is sample and p is probability.

Ans 7 (a) It is easy for all statisticians to work with normal distributions, almost all tools have assumed that there is normal distribution.

(b) psychological variables are normally distributed. Driving, riding, playing, love, IQ etc. are normal distributed.

Ans 8 It is given that

• errors are independent of each other.
• there are 5 errors per 10000 feet

Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. Both conditions given are satisfied here, so we can use Poisson distribution.