1. In a standard normal distribution, find the following values: a. The probability that a given z score is less than-2.67 b. The probability that a given z score is between 1.55 and 2.44 C. The z scores that separates the most inner (middle) 82% of the distribution to the rest d. The z score that separate the lower 65 % to the rest of the distribution 2. According to a survey conducted in the Republic of KXW, the income distribution of all its union workers is normal with an average of 51000 KXW dollars and a standard derivation of 2700 KXW dollars. If a single worker is selected at random, use the normal distribution and compute the following: a. The probability that he/she earns more than 57000 KXW dollars b. The probability that he/she earns less than 47000 KXW dollars c. The probability that he/she earns between 47000 KXW dollars and 57000 KXW dollars 3. According to a survey conducted in the Republic of KXW, the income distribution of all its union workers is normal with an average of 51000 KXW dollars and a standard derivation of 2700 KXW dollars. a. What salary separates the lower 90% earners to the rest of this population? b. What salaries separate the middle 95% earners to the rest of the population? 4. The mean amount of money that U.S adults spend on food in a week is $140 and standard deviation is $42. Random samples of size 40 are drawn from this population and the mean of each sample is determined. a. Find the mean and standard deviation of the sampling distribution of sample means. b. What is the probability that the mean amount spent on food in a week for a certain sample is more than $143? c. What is the probability that the mean amount spent on food in a week for a certain sample is between $138 and $143? 5. According to the Uniform Crime Report, 70% of murders are committed with a firearm. Supposed that 50 murders are randomly selected, use the normal approximation to the binomial to a. Compute the mean and standard deviation b. Approximate the probability that at least 30 murders were con c. Approximate the probability that more than 30 murders were committed using firearm. d. Approximate the probability that exactly 30 murders were committed using firearm. e. Approximate the probability that between 30 and 37 murders, inclusive, are committed using a hitted using firearm. firearm. Chapter 6 6. In a random sample of 28 SUVS, the average fuel cost was $4235. Prior experiment revealed a population standard deviation of $902. Construct the 90% confidence interval for the population mean. Interpret the result. Assume that the annual fuel cost are normally distributed. 7. In a random sample of 28 SUVS, the average fuel cost was $4235 with a sample standard deviation of $902. Construct the 90% confidence interval for the population mean. Interpret the result. Assume that the annual fuel cost are normally distributed. 8. How large must a sample be in order to estimate the average salary of all History professors within $558 of the population average with an 82% confidence interval? Prior experiments estimate the population standard deviation to be $ 4200. 9. In a survey of 1022 U.S. adults, 779 think that the United States of America should put more emphasis on producing domestic energy from solar power. a. Find the point estimate for the population proportion(p) b. Construct an 80% confidence interval for the population proportion (p) and interpret the result. c. What would happen to the confidence interval if a larger sample size were to be drown? 10. You wish to estimate, with a 99% confidence, the population proportion of U.S adults who think they should be saving more money. Your estimate must be accurate within 5% of the population proportion. a. No preliminary estimate is available. Find the minimum sample size needed. b. Find the minimum sample size needed, using a prior estimate that found that 65% of U.S adults think that they should be saving more.