Objective type problem on Sampling Distribution.

1. The Central Limit Theorem is significant in statistics because

1) For a large n it says the population is approximately normal.

2) For any population it says the sampling distribution of the sample mean is approximately normal regardless of the sample size.

3) For a large n it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

4) For any sized sample it utters the sampling distribution of the sample mean is approximately normal.

 2. Which of the subsequent statements about the sampling distribution of the sample mean is incorrect?

1) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n ≥ 30).

2) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.

3) The mean of the sampling distribution of the sample mean is equal to μ.

4) The standard deviation of the sampling distribution of the sample mean is equal to σ.

3. Supposing a sample of n = 50 items is drawn from a population of manufactured products and the weight X and of each item is recorded. Previous experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. Which of the subsequent is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

1) The nasty of the sampling distribution is 6 ounces.

2) The standard deviation of the sampling distribution is 2.5 ounces.

3) The shape of the sample distribution is approximately normal.

4) All of the above are correct.

4. The average score of entirely pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Supposing 36 golfers played the course today. Find the probability which the average score of the 36 golfers exceeded 71. 

5. The distribution of the number of loaves of bread sold per day by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves. Supposing a random sample of n = 40 days has been selected. describe what is the approximate probability that the average number of loaves sold in the sampled days exceeds 7,895 loaves?