Can this distribution be approximated by a normal distribution Why?
The normal distribution can be used as an approximation to the binomial distribution, under certain circumstances, namely: If X ~ B(n, p) and if n is large and/or p is close to ½, then X is approximately N(np, npq)
Can the sampling distribution be approximated by the normal distribution?
Because our sample size is greater than 30, the Central Limit Theorem tells us that the sampling distribution will approximate a normal distribution.
How do you determine if a distribution is approximately normal?
The most obvious way to tell if a distribution is approximately normal is to look at the histogram itself. If the graph is approximately bell-shaped and symmetric about the mean, you can usually assume normality. The normal probability plot is a graphical technique for normality testing.
Can a normal approximation be used for a sampling distribution of sample means from a population?
A sampling distribution of sample means has a standard deviation equal to the population standard deviation, σ. The larger the sample size, the better the normal distribution approximation will be. Therefore, the correct answer is: No, because the sample size is less than 30.
What is NP and NQ in statistics?
When testing a single population proportion use a normal test for a single population proportion if the data comes from a simple, random sample, fill the requirements for a binomial distribution, and the mean number of success and the mean number of failures satisfy the conditions: np > 5 and nq > n where n is the …
What does approximately normal distribution mean?
Intelligence test scores follow an approximately normal distribution, meaning that most people score near the middle of the distribution of scores. For example, on the IQ scale, about two-thirds of all scores fall between IQs of 85 and 115, and about 95\% of scores fall between 70 and 130.
Can a normal approximation be used for a sampling distribution of sample means from a population with μ 74 and σ 14 when n 25?
The sampling distribution of the mean approaches a normal distribution as the sample size n increases. The random variable ¯¯¯¯¯X has a different z-score associated with it from that of the random variable X. The mean ¯¯¯x is the value of ¯¯¯¯¯X in one sample. μx = μ¯¯¯x μ x ¯ (mean of X = mean of ¯¯¯¯¯X . )
Can a normal approximation be used for a sampling distribution of sample means from a population with μ 47 μ 47 and Σ 9 Σ 9 when N 4 N 4?
Therefore, the correct answer is “Yes, because the sample size is at least 30.”