A simple random sample of size n = 76 is obtained from a population with μ = 60 and o=2. Does the population need to be normally distributed for the sampling distribution of x to approximately normally distributed? Why? What is the sampling distribution of X? G Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? O A. Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. O B. No because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. O C. No because the Central Limit Theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. O D. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. What is the sampling distribution of X? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.) OA. The sampling distribution of x is normal or approximately normal with µ = O B. The sampling distribution of x is uniform with µμ- = and %x and o-=

A simple random sample of size n= 32 is obtained from a population that is skewed left with u = 58 and o = 10. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? O A. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. O B. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size,n. O C. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. O D. No. The central limit theorem states that only if the…

3. For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n= 65 and p = 0.7 a. Normal approximation is not suitable. b. Normal approximation is suitable.

time, i.e. P(μx-ox ≤ x ≤ μx + 0x). 3. Suppose that people heights are normally distributed with mean of 170 cm and standard deviation of 6 cm. a) What proportion of people are between 165 cm and 175 cm tall? b) Find the minimum ceiling of an airplane such that at most 5% of people walking down the aisle will have to duck. E c) Find the probability that the average height of a random sample of 49 people is greater than 172 cm. 80 F3 4 R % 5 T F6 Y 1 & 7 K ard deviation of the expected U 8 DII

For the population whose distribution is Uniformly distributed from 30 to 52, random samples of size n = 39 are repeatedly taken. Compute u and round to two decimals. Use this value to find the following. Round answers to three decimals if needed. Answers of 0 and 1 are possible due to rounding. a. P(40 < < 43): b. The 25th percentile for sample means: Submit Question

A simple random sample of size n = 50 is obtained from a population that is skewed left with μ=41 and o=7. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? O A. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. OB. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. O C. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. O D. Yes. The central limit theorem…

The heights of fully grown trees of a specific species are normally distributed, with a mean of 54.5 feet and a standard deviation of 5.75 feet. Random samples of size 19 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution. The mean of the sampling distribution is u- %3D The standard error of the sampling distribution is o, = X. (Round to two decimal places as needed.) Choose the correct graph of the sampling distribution below. O A. В. OC. 2. 51.9 54.5 57.1 43.0 54.5 66.0

Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 20,000 and whose population proportion with a specified characteristic isp=D0.2. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1 - p)< 10. O B. Not normal becausens0.05N and np(1- p)< 10. O C. Not normal because ns0.05N and np(1-p)2 10. OD. Approximately normal because ns0.05N and np(1 - p) 2 10. Determine the mean of the sampling distribution of p. HA = 0.2 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. GA = (Round to six decimal places as needed.)

For the population whose distribution is Uniformly distributed from 35 to 45, random samples of size n = 34 are repeatedly taken. Compute u and round to two decimals. Use this value to find the following. Round answers to three decimals if needed. Answers of 0 and 1 are possible due to rounding. a. P(41 < a < 43): b. The 15th percentile for sample means: Submit Question r

Peter is trying to figure out the sample size for the data set he wants to collect. He is considering having the bound on the error of estimation to be either 3.5 or 4.5. Explain to Peter the impact these different errors will have on his sample size.