This question contains 16 short questions covered Unit 4. Each part of question carries 2 mark. Your answer should be short and precise. After study this question, you should be able to ' understand the fundamental concept of standard normal, normal distribution and normality; sample distributions of the sample mean and standard derivation, and condence interval covered by Unit 4; calculate the related parameters and confidence interval of one population mean. (I) A northeastern college has an enrollment of 2835 female students. Records show that the mean height of these students is 652 inches and that the standard deviation is 2.8 inches. The following table shows frequency and relative-frequency data for these heights. We assume that the distribution of heights is approximately normal, you can use the table below to estimate areas under the associated normal curve (that is, under the normal curve that has parameters u = 65.2 and o = 2.8). Estimate the percentage under the associated normal curve between 65 and 70. [2] (2) Use statistical Table II in your Textbook to nd the area of the shaded area under the standard normal curve. [2] (3) A normal probability plot is given below for the weekly incomes (in dollars) of a sample of engineers in one town. Interpret about the normality of the incomes of engineers in this town. [2] Normal Score 7m II] 91]] llIl ll 12m13m 14m 11m Weev'lncm (Dollars) (4) Given population data: 3, 4, 5, 6, 7. (a) Use the population data to construct a table that gives the sample means of sample size n = 2. [2] (b) Draw a dotplot for the sampling distribution of the sample mean. [2] (c) Find the probability that the sample mean will equal the population mean. [2] (d) Find the probability that the sampling error made in estimating the population mean by the sampling mean will be 0.5 or less (in magnitude). (That is, the absolute value of the difference between the sample mean and the population mean is at most 0.5.) [2] (5) Suppose that p represents the mean height for a population of people. Suppose that you use a sample mean f, to estimate p. (a) Explain what is meant by sampling error in this situation. [2] (b) Why does 3? vary from one sample to another sample? [2] (c) How can you reduce the likely sampling error? [2] (6) The mean height for a population of people is 65 inches. Suppose that you pick a sample of 50 people and determine the sample mean :2. You then repeat this procedure three more times. You learned in class that #33 = p. Explain whether the mean of the four sample means will be equal to the population mean of 65 inches. Why or why not? (7) The weights of people in a certain population are normally distributed with a mean of 154 lb and a standard deviation of 23 lb. (a) Determine the distribution of the sample mean and standard deviation for samples of size 4. [2] (b) Comment on whether the distribution of f is normal or approximately normal. Justify your answer. [2]