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8.1 Sampling Distribution of the Sample Means 9. The scores of students on the ACT college entrance examination in a recent year had a Normal distribution with mean p : 13.6 and a standard deviation of o = 5.9. {a} What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher? [bl Now take a simple random sample of 50 students who took the test. What are the mean and standard deviation of the sample mean score a" of these 50 students? [c] What is the probability that the mean score of these students is 21 or higher? 1D. The Annual Demographic Supplement to the current Population Survey interviewed more than 123,000 people in March 2001. The Census Bureau reports that the mean income of the Hispanic males interviewed was 522311. The mean income for the non Hispanic white males interviewed was $41,798. ls each of the bold numbers a parameter or a statistic? 11.13. survey conducted by Black Flag asked whether or not the action of a certain type of roach disk was effective in killing roaches. TENS of the respondents agreed that the roach disk was effective. The number 19% is a A. parameter. E. population. C. statistic. D. sample. 12. The weightsI in pounds, of Portuguese Water Dogs are normally distributed with mean 45 and standard deviation 3. a} If one dog is selected at random, find the probability that his weight is within 1 pound of the mean weight of 45. b] If 40 dogs are randomly selected, nd the probability the sample mean weight is within 1 pound of the mean weight of 45. cl If EC- dogs are randomly selected, find the probability that the sample mean weight is greater than 4? pounds. 13. The weights of Granny Smith apples from a large orchard are Normally distributed with a mean of 330 gm and a standard deviation of 28 gm. a] A single apple is selected at random from this orchard. What is the probability that it weighs more 400 gm? b} Three apples are selected at random from this orchard. What is the probability that their mean weight is greater than 40D gm? 14. Suppose a sample of 50 MP3 players is drawn randomly from a population of MP3 players and the weight, k, of each MP3 playeris recorded. Prior experience has shown that the weight of a single MP3 player has a mean of 6 ounces and a standard deviation of 2.5 ounces. 3) Describe the shape of the sampling distribution of i- and justify your answer. b) What is the mean and standard deviation of the sampling distribution