xtending the Concepts 15. Recall that for use of a normal distribution as an xim

Question

xtending the Concepts 15. Recall that for use of a normal distribution as an ximation to the binomial distribution, the conditions np 5 and nq 5 must be met. For each given probability, compute the minimum sample size a, p= 0.1 b, p= 0.3 c, p 0.5 d. p 0.8 e, p=0.9 eeded for use of the normal approximation. Summary . A normal distribution can be used to describe a variety of variables, such as heights, weights, and temperatures. A normal distribution is bell-shaped, unimodal. c, and continuous; its mean, median, and mode are equal. Since each normally distributed variable has its own distribution with mean and standard deviation , mathematicians use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. Other approximately normally distributed variables can be transformed to the standard normal distribution with the formula A normal distribution can be used to solve a variety of problems in which the variables are approximately normally distributed. (6-2) A sampling distribution of sample means is a distribution using the means computed from all possible random samples of a specific size taken from a population. The difference between a sample measure and the corresponding population measure is due to what is called sampling error. The mean of the sample means will be the same as the population mean. The standard deviation of the sample mean will be equal to the population standard deviation divided by the square root of the sample size. The central limit theorem states that as the sample size increases without limit, the shape of the distribution of the sample means taken with replacement from a population will approach a normal distribution. 6-3) binomial distribution. For a normal distribution to be used as an approximation, the conditions n/2 5 and nq 5 must be met. Also, a correction for continuity may be used for more accurate results. (6-4) . A normal distribution can be used to approximate other distributions, such as a 6-49

Explanation / Answer

(a)
np >= 5
n >= 5/0.1
n >= 50

Sample size = 50

c)
np >= 5
n >= 5/0.5
n >= 10

Sample size = 10

e)
np >= 5
n >= 5/0.9
n >= 6

nq >= 5
n >= 5/0.1
n >= 50

Sample size = 50

Related Questions

Navigate

• Browse (All)
• Browse X
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.