hw5 - Find the indicated region under the standard normal...

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Unformatted text preview: Find the indicated region under the standard normal curve. 21=D, 2;} =1.6 Find the area that corresponds to the two z—scores. Then subtract the smaller area from the larger area. Alternatively, you can use the normalc df function on a graphing calculator. The area under the standard normal curve in the shaded region is (Round to four decimal places.) Find the indicated area under the standard normal curve. To the left of: = 3.00 Choose the correct probability. Find the area to the left of the z-score using a z-score table or using the normalcdf function on a graphing calculator. Find the indicated area under the standard normal curve. To the right ofz = -D.ED Choose the correct probability. 0 a. 0.420? C) b. 0.?645 Use the z-score table to find the area to the left ofz = -D. 20. Subtract that area from 1 to find the area to the right of the z—score. Alternatively, use the © [1- 0.5?93 normalch function on a graphing calculator. O c. n.21o4 Find the indicated arm under the standard normal curve. Betweenz= I] andz= 0.8 Choose the approximate area. 0 a. 0.1441 Find the areas corresponding to the two 2: scores. Find their difference. Alternatively, use the normalch function on a graphing calculator. Find the indicated area under the standard normal curve. Betweenz= —l.SS andz= 2.30 Choose the approximate probability. 0 a. mass 0.0631 Find the arms corresponding to the two 2 —scores. Then find their difference. Alternatively, use the normalcdf function on a graphing calculator. Find the probability of z occurring in the indicated region. Use the Standard Normal table to find the arm that corresponds to the z-score. The arm is equivalent to the probability ofz occurring in the region. Alternatively, use the normalcdf function on a graphing calculator. The probability of z occurring in the shaded region = D. 3359 . (Round to four decimal places.) Find the probability of Z occurring in the region. 2I 21 = -2.0 Find the arm that corresponds to the two z—scores. Then subtract the smaller arm from the larger area. The difference in areas is equivalent to the probability The probability ofz occurring in the shaded region is 0.8304 _ of z occuring in the region between the z-scores. Alternatively, use the (Round to four decimal places.) norrnalcdf function on a graphing calculator. Find the probability using the standard normal distribution. P(-E|.83 < z c: o). Find the area that corresponds to the two z-scores. Then subtract the smaller arm from the larger arm. The difference in arms is equivalent to the probability P(-E|.83 : z q: o) = (Round to four decimal places.) of z occuring in the region. Alternatively, use the norrnalcdf function on a graphing calculator. Find the indicated probability using the standard normal distribution. P(-l.55 <2 {1.55) Choose the correct probability. Ci) a. ESTES 0.4395 Find the area to the left ofz= -l.55 and to the left ofz = 1.55. Then subtract the arm to the left of z = —1.55 from the arm to the left of: = 1.55. Alternatively, use the norrnalcdf function on a graphing calculator. Assume the random variable x is normally distributed With rnmn ,u. = 82 and standard deviation 0' = 11. Find the probability. Prx < so) Pr: < 60) = (Round to four decimal places.) Find the percentage of the arm to the left of the z-score corresponding to x= 60. 1—.“ CF . Use the formula 2 = Assume the random variable x is normally distributed with mmn it = 63.6 and and standard deviation 0' = 2.5. Find the indicated probability. Prx > T0) Find the arm to the right of the z-score corresponding to x = 70. P(x > T0) = ooosz (Round to four decimal places.) Use the formula 2 = x—rt J . Assume the random variable x is normally distributed with mmn it = 63.6 and standard deviation 0' = 2.5. Find the indicated probability. P(64 < x < 68) Find the area between the two z-scores corresponding to x = 64 and X = 63. P(64 :1 x =1 68) = 0.39?2 (Round to four decimal places.) Use the formula Z = rest J . Suppose the height of a population is normally distributed with a mean of 69. 2 inches and a standard deviation of 2.9 inches. A member of this population is randomly selected. Find the probability that the person's height is more than TEI inches. Probability that the member's height is more than TD inches = 0.3913 (Round to four decimal places.) Use az-score table to find the percentage of the area to the right of the z-score corresponding to a height of TEI inches. Suppose that a population of adults is surveyed to measure the number of hours per week spent on home computers. In the survey, the number ofhours is normally distributed with a mean of 7" hours and a standard deviation of 1 hour. Find the probability that a randomly selected adult spends between 7".3 hours and 9.7" hours on a home computer per week. 130.3 < hours on home computer < 9.?) = .3?86 (Round to four decimal places.) Calculate the corresponding z—scores with the following formula. Number of hours — an Number of hours Standard deviation z: Find the arm bounded by the two z—scores. Suppose that a population of adults is surveyed to mmsure the number of hours per week spent on home computers. In the survey, the number of hours is normally distributed with a mean of 7 hours and a standard deviation of 1 hour. Find the percent of the adults that spend more than 7.3 hours on a home computer per week. If 2TB adults are randomly selected, about how many would you expect to say they spend less than 6.7" hours per week on a home computer? Percent of adults who spend more than 7".3 hri‘week on a home computer = 33.21 (Round to the nmrest hundredth of a percent.) _ _ _ Calculate the corresponding z-score With the follovving formula. If 27”] adults are randomly selected, about how many would you expect to say they spend less Number of hours — Mean number of hours than 6.? hrsi’week on a home computer? Standard deviation 103' 2 adults Find the area to the right of the z-score. Convert the area to a percent by (Round to the nearest tenth.) multiplying by loo. First, find the z—score corresponding to 6.? hoursfweek. Find the area to the lefi of the z-score under the standard normal curve. Then multiply the area by the number of adults selected. Use the Standard Normal Table to find the z—score that corresponds to the cumulative area. If the arm is not in the table, use the entry closest to the area. If the arm is halfway between two entries, use the z-score halfway between the corresponding z-scores. DD? 2= (Round to the nmrest hundredth.) The arm to the left of the z—score you are trying to find is Ill]? Using the table, find the arm that is closest to ELEIT; this arm corresponds to the correct z-score. Find the indicated z-score shown in the graph. Ara=040l3 Using the table, find an ara that is closest to the given ara. Find the z-score Z = corresponding to that ara. Alternatively, use the invNorrn function on a (Round to the nearest hundredth.) _ hm calculator Find the indicated z-score shown in the graph. Ara= 0.6fi23 Using the z-score table, find an area that is closest to the given area. Then find Z = the z-score corresponding to that area. Alternatively, use the invNorm function (Round to the narest hundredth.) 011 El graphing calculator. Find the z-score that has 64. 8% of the distribution's area to its left. 2 = Using the table, find the arm that is closest. to 54 8% in deeirnal forrn. Then [:leund tn the nearest. fincl the z—score that corresponds to that area. Alternatively, use the invNorm function on a graphing calculator. Find the z-score that has 70% of the distribution's area between 2 and -z. Remember, the symmetry of the standard normal curve says the area to the left i z = of 72 is equal to the area to the right ofz. The total area is 1 a on. Find half of that area. Then use the symmetry of the normal curve to find the z-seore with (Round to the narest hundredth.) area D 14 to the fight You sell a brand of tires that has a life expectancy that is normally distributed, with a man of 55000 miles and a standard deviation of 2500 miles. You want to give a guarantee for free replacement of tires that don't war well. How should you word the guarantee if you are willing to replace 10% of the tires you sell? Tires that war out by 51800. miles will be replaced free of charge. (Round to the nearest hundred miles.) Find the z-score corresponding to area 0.10 to the left of 2. Replace this score and the man and standard deviation in the formula for z. Solve for the value, 2:. using the formula below. A population has a man ,u. = 100 and a standard deviation 0' = 15. Find the man and the standard deviation of a sampling distribution with the sample size n. n=240 Man of the sample = (Type an integer.) Standard deviation of the sampling distribution = . R 13 th fin [1i .1: , . L131 th ula . (Round to the nearest hundradth') ernem er e samp g stn ution man is eq to e pop tion man. The standard deviation of the sampling distribution of the sample mans, 0'3: , is equal to the population standard deviation, 0' , divided by the square root of n. 0'}: i v”? The prices ofa certain piece of electronic equipment are normally distributed, with a man of $355 and a standard deviation of $19. Random samples of size 55 are drawn from this population and the man of ach sample is determined. Use the Central Limit Theorem to find the man and standard error of the mean of the sampling distribution. Man of the sampling distribution = $ (Round to the narest dollar.) 0' Standard error ofthe sam lin distribution = 5_.56 Recall that CI“ = ' . p g Recallthattti=tL " 1’? (Round to the narest cent.) The per capita consumption ofa food item by people in a certain country was normally distributed with a man of 115 lb and a standard deviation of 37".9 lb. Random samples of size 19 are drawn from this population and the mean of each sample is determined. Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. The mean ofthe sampling distribution = lbs The standard error of the sampling distribution = lbs (Round to the nearest hundredth.) The standard deviation of the sampling distribution of the sample mans is found using the following formula. The man of the sample mans is equal to the population man. 0' Suppose the population man annual salary for a certain profession is Iv. = $33300. A random sample of 55 professionals is drawn from this population. What is the probability that the man calculate me 2.5mm for f = Minn, Find the area to 111131313, ofthe 2—score; salary Ufthe sample, f, is less than $37799? Assume 0' = $3199. this value is equivalent to the probability. Use the following formula to find the Z-SCDI’E. Hr < arson) = o.oo34 T—F‘ (Round to four decimal places.) 2 = mix-W The man height of women in a certain population (ages 20-29) is .u = 66 inches. A random sample of4U women in this age group is selected. What is the probability that f, the man for the sample, is grater than 66.9 inches? Assume 0' = 2.?5 inches. E'ind the probability that the man height of the sample is grater than 66.9 inches. 0.0192 (Round to four decimal places.) 0' The standard deviation of the sample mans is denoted by C"; = fl . Convert the man height f = 66.9 to az-score using the formula 2 = f— F'- o’l/‘v' 11 Don't forget that the area to the right of a z-score is equal to 1 minus the area to the lefi ofa z-score. Match the binomial probability with the corresponding statement. . Refer to a z-score table to find the area to the left of thez score. Hrs 53) Choose the correct statement. © 3- P(there are at most 53 successes) O b. P(there are more than 53 successes) C) c pahere are less than 53 successes) Review the interpretations for the inequality symbols. "Less than" and "grater than" do not include the number 53. "At lastII and "at most" include the number 0 9- P(there are at last 53 successes) 51 Use a correction for continuity and choose the correct normal distribution statement for the given binomial probability statement. 13(x > 6) Choose the correct statement. @ a. 13(x > 6.5) o b. 13(x > do) Apply a continuity correction. Since the inequality is a strict inequality, it does 0 c. P(x > 5.5) not include the probability ofx = 6. Either subtract 0.5 from the left endpoint of 0 d. 1:3 > To) this area or add 0.5 to the right endpoint ofthis area. Suppose 52% ofa certain population say that chocolate chip is their favorite cookie. You randomly select 33 people from the population and ask each if chocolate chip is his or her favorite cookie. Find the rela ed probabilities. Use the normal distribution to approximate the binomial distribution. Find the pro oability that exactly 20 people will say chocolate chip is their favorite. 0.0341 (Round to four decimal places.) Find the probability that at least 20 people will say chocolate chip is their favorite. To apply the Bonn-an curfew-0n to "exactly 20.. means you want the area D'EUM (Round to four deem places) between x = 20 minus 0.5 and x = 20 plus 0.5. Find the area under the normal curve between 19.5 and 20.5 with a mean equal to rip, a standard deviation Find the probability that fewer than 20 people will say chocolate chip is their favorite. equal to 1} n q . 0.?926 (Round to four decimal places.) 'At least 20' means 20 or more, so applying the continuity correction means you want to find the area under the normal curve to the right of 19.5 with a mean USE the faCt that PCfE-“WEI' than 2E0=1 - F'Cnat fewer than 20)=1 - Hat least equal to up, a standard deviation equal to 1} n q . 2'33" ...
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hw5 - Find the indicated region under the standard normal...

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