Please help with the assignment (will give postivie rating):
cl 3. A. CI Consider a parent population with mean 75 and a standard deviation 7. The population doesn't appear to have extreme skewness or outliers. lIllI'hai: are the mean and standard deviation of the distribution of sample means for n = 40? (2 points) . What's the shape of the distribution? Explain your answer in terms of the Central Limit Theorem. (1 point) . What proportion ofthe sample means of size 40 would you expect to be 77 or less? If you use your calculator, show what you entered. (1 point) . Draw a sketch of the probability you found in part C. (1 point) Suppose over soveral years of orfeng AP Statistics, a high school finds that final exam scores are nonnally distributed with a mean of 7B and a standard deviation of 6. . Whit III the mean, standard deviation. and shape ofthe distribution of x-bar torn = 50? (2 points) Whlt'i the pl'blblllt'f I sample I!" m WI" I'll\" I l'lllll'l greater than an? [1 point] Sketch the dlltl'illlltldn curve for part B. ll'ldwll'lg the It'll thlt represents the problblllty you found. (1 point) Suppose college faculty members wltl'l the rank Of professor at two-year Institutions earn an average Of $52,500 par year wltl'l a standard deviation or $4,000. In an attempt to verify this salary level, a random sample Of 50 professors was selected frDI'l'l a personnel database for all two-year institutions In the United States. What are tin mean and standard deviation of the sampling distribution for n - 6|}? (2 points) What's the shape of the sampling distribution for n - do? (1 point] calculate the probability the sample mean ebb" le greater than assume. (1 point) If you drew a random sample with a mean of sssmoo, would you consider this sample unusual? What oonelualone might you draiiiiiI (1 point) 4. AI Cs A manufacturer of paper used for packaging requires a minimum strength on p0unds per square inch. To check the quality of the paperr a random sample of ten pieces of paper ls selected each hour from the previous hour's production and a strength measurement Is recorded for each. The distribution of strengths is known to be normal and the standard deviation, computed from many samples, Is known to equal 2 pounds per square inch. The mean is known to be 21 pounds per square inch. 1Iiiihat are the mean and standard deviation of the sampling distribution for n = 1m (2 points} . 1lliihat's the shape of the sampling distribution for n = 10? (1 point} Draw a random sample of size 10 from this distribution and compute the mean of the sample, using the randl'ilorm function on your calculator. On a TI-83l84 store the values In L1: [nan] randnnnn{21,2,1oi [L1]. (in a 11-39 Store the values in lieu: seofrandorm(21,2),x,1,1ti,1) -> ilstI. On the 11-83,!84 you can then et the mean of the values Iw doing 1Var stats en tire values in L1. Then Press arrow to sale, select l-Var stats, Press than BE un- Dn the 11-89 you can then get the mean of the values by doing :l.-'llar Stats on the values In lieu. Enter Llst Editor. then press F4: tit-Var State... Enter list1 as your list and press ENTER twice to do the calculation. Wt HOV\"! I" your IIII'IHII values. Whit If. U\" I'I'IOII'I and sample standard HIViIOII 0" !" sample? Compare l with \"I. II'IIII'I Il'ld ItIl'ldiIl'd dWlltIDl'I Of \"I. parent population. and explain why 'l' dlllt Or \"I. same. (2 points) Using the mean and standard deviation of the sampling distribution (from part A). calculate the probability of getting a sample mean less than what you got. If you use a calculator, show what you entered. (2 points] Suppose a random sample Of :1 B 25 Observations is SEIECtEd fl'Gl'l'l a normal DDDUIGUOI'I. with mean 106 and standard deviation 12. Find the probability that a-bar aseeeds no. Show the mean and standard deviation you used. (2 points] Find the probability that the sample mean deviates from the population mean - toe by no more than 4. {1 point} Sketch the probability distribution from part a, showing the area that represents the probability you found. (1 point]
