Follow the directions in Chapter 6 (Comparing Data Characteristics to Theoretica
ID: 3063545 • Letter: F
Question
Follow the directions in Chapter 6 (Comparing Data Characteristics to Theoretical Properties and Constructing the Normal Probability Plot) to answer this question. (10 points)
Assuming that the “age” variable for the individuals in the Patients' dataset is normally distributed, what is the probability that the age of a patient in this dataset:
Is less than 45?
Is greater than 55?
Lies between 45 and 55?
Length of Stay ICU Days Age (Years) Sex (M/F/U) Principal Payer Total Chges Drug Charges Lab Charges Imaging Charges RT Chge 3 0 78 F CARE $ 5,418.85 $ 68.70 $ 273.50 $ 832.00 $ 660.85 3 0 74 F CARE $ 4,575.10 $ 58.65 $ 439.50 $ 725.00 $ 276.50 11 0 89 M CARE $ 12,031.18 $ 230.28 $ 816.50 $ 187.00 $1,312.30 3 0 81 M CARE $ 3,617.84 $ 142.89 $ 387.00 $ 93.50 $ 231.95 9 0 87 F CARE $ 12,806.88 $ 889.23 $ 795.50 $ 827.50 $1,526.35 3 0 65 CARE $ 5,295.55 $ 102.50 $ 837.00 $ 959.50 $ 177.45 3 0 90 M CARE $ 3,453.21 $ 122.15 $ 323.00 $ 103.00 $ 23.45 3 0 61 M BC $ 1,760.03 $ 161.18 $ 35.00 $ - $ 303.85 3 0 90 F CARE $ 3,290.40 $ 235.65 $ 243.00 $ 117.50 $ 446.55 5 0 78 M CARE $ 6,253.65 $ 103.05 $ 487.50 $ 941.00 $ - 3 0 78 F CARE $ 3,896.16 $ 229.06 $ 222.00 $ 93.50 $ 477.05 2 0 71 M CARE $ 1,795.35 $ 52.05 $ 58.00 $ 216.00 $ 39.30 3 0 76 M CARE $ 9,265.17 $ 211.37 $1,626.50 $ 1,255.00 $ 827.65 3 0 76 F CARE $ 3,282.90 $ 298.40 $ 381.50 $ 214.00 $ 476.75 5 0 79 F CARE $ 9,565.83 $ 477.03 $ 974.00 $ 214.00 $2,017.80 3 0 72 M CARE $ 3,782.15 $ 166.85 $ 345.00 $ 93.50 $ 253.60 4 1 72 M CARE $ 6,384.28 $ 342.98 $ 644.85 $ 307.50 $ 605.30 3 0 64 M CARE $ 4,904.25 $ 208.65 $ 768.00 $ 832.00 $ 369.60 2 0 72 F CARE $ 4,169.92 $ 545.15 $ 375.50 $ 557.00 $ 803.77 3 0 69 F CARE $ 5,204.41 $ 510.01 $ 870.50 $ 158.00 $ 599.05 4 0 63 M HMO $ 6,740.00 $ 480.20 $1,091.50 $ 925.50 $ 734.40 1 0 78 M CARE $ 5,016.44 $ 401.44 $ 630.00 $ 158.00 $ 246.75 2 0 83 M CARE $ 4,178.94 $ 604.49 $ 433.50 $ 1,188.50 $ 217.05 3 0 62 F OTHR $ 4,105.26 $ 90.46 $ 222.00 $ 725.00 $ - 4 0 71 M CARE $ 4,717.30 $ 120.90 $ 496.00 $ 631.50 $ - 6 0 83 F CARE $ 6,598.92 $ 380.17 $ 386.00 $ 832.00 $ 226.15 2 0 63 F OTHR $ 1,633.85 $ 20.85 $ 207.00 $ 93.50 $ 88.30 1 0 83 M CARE $ 2,200.85 $ 21.00 $ 176.00 $ 117.50 $ 202.75 4 0 76 F CARE $ 7,461.54 $ 508.34 $1,082.50 $ 1,071.50 $ 340.65 5 0 79 M CARE $ 11,413.23 $ 1,149.88 $1,335.50 $ 267.00 $1,442.15 3 0 65 M CARE $ 5,607.55 $ 230.50 $ 969.35 $ 738.50 $ 289.15 2 0 79 M CARE $ 4,850.62 $ 172.52 $ 867.00 $ 845.50 $ 206.05 4 0 74 M CARE $ 7,102.49 $ 259.09 $ 881.00 $ 780.00 $ 773.85 15 0 63 M OGVT $ 13,615.69 $ 438.84 $1,930.00 $ 912.00 $1,911.70 3 0 84 M CARE $ 5,069.18 $ 282.90 $ 476.50 $ 832.00 $ 345.80 6 0 90 F CARE $ 6,536.07 $ 122.85 $ 651.00 $ 947.50 $ 458.05 4 0 73 F CARE $ 7,401.25 $ 216.90 $ 971.50 $ 845.50 $ 562.10 2 0 81 M CARE $ 3,744.34 $ 176.24 $ 394.00 $ 1,291.50 $ 80.00 5 0 75 F CARE $ 8,653.68 $ 246.63 $ 859.00 $ 767.00 $ 942.10 9 0 87 F CARE $ 14,423.21 $ 527.63 $2,138.00 $ 925.50 $1,069.00 3 0 70 M CARE $ 3,742.30 $ 112.95 $ 396.50 $ 93.50 $ 340.65 3 0 73 F CARE $ 5,514.09 $ 368.34 $ 874.50 $ 200.50 $ 371.55 5 0 77 M CARE $ 7,390.15 $ 331.25 $ 696.00 $ 825.00 $ 661.90 5 0 71 M CARE $ 9,358.20 $ 491.35 $1,223.50 $ 1,230.80 $ 736.95 7 0 76 M CARE $ 14,570.29 $ 286.74 $1,090.00 $ 939.00 $ 921.80 4 0 49 F CAID $ 4,526.43 $ 203.98 $ 378.50 $ 725.00 $ 608.95 6 0 78 F CARE $ 6,846.77 $ 162.57 $ 657.50 $ 93.50 $ 181.00 2 0 86 M CARE $ 2,927.62 $ 145.42 $ 606.50 $ 107.00 $ 543.10 3 0 67 M CARE $ 4,404.13 $ 161.78 $ 630.00 $ 93.50 $ 491.10 6 0 69 M CARE $ 8,056.36 $ 331.66 $ 642.00 $ 767.00 $ 367.15 8 0 73 F CARE $ 10,703.34 $ 618.64 $1,297.50 $ 692.50 $ 958.30 4 0 88 F CARE $ 16,458.95 $ 813.55 $1,050.50 $ 971.50 $2,114.60 5 0 67 M INS $ 4,770.10 $ 236.30 $ 747.00 $ 93.50 $ - 8 0 69 M CARE $ 15,282.57 $ 1,704.77 $1,860.00 $ 1,153.00 $2,221.30 7 0 77 M CARE $ 10,105.30 $ 597.30 $1,251.00 $ 1,304.50 $ 877.00 8 0 64 F CAID $ 7,871.29 $ 606.64 $ 550.00 $ 200.50 $ 725.05 3 0 76 M CARE $ 3,411.10 $ 124.70 $ 356.50 $ 187.00 $ 93.15 12 0 64 F CAID $ 10,962.17 $ 712.67 $ 697.00 $ 321.00 $1,144.35 2 0 41 M SELF $ 7,374.27 $ 361.47 $ 600.50 $ - $ 554.00 5 0 49 M CAID $ 7,788.51 $ 478.85 $ 610.00 $ 736.50 $ 500.85 5 0 59 M BC $ 8,191.10 $ 661.65 $ 800.00 $ 117.50 $ 445.30 3 1 81 M CARE $ 11,117.35 $ 142.35 $ 318.00 $ 736.50 $ 50.85 2 0 74 F CARE $ 5,624.54 $ 149.69 $ 542.00 $ 1,348.50 $ 326.40 4 0 77 F CARE $ 4,574.92 $ 159.82 $ 186.50 $ - $ 612.50 3 0 78 F CARE $ 3,644.36 $ 126.46 $ 220.50 $ - $ 30.90 2 0 73 F CARE $ 2,937.92 $ 50.67 $ 268.00 $ 673.50 $ 134.65 6 0 67 M INS $ 3,944.78 $ 602.98 $ 462.00 $ 93.50 $ - 3 0 80 M CARE $ 6,366.10 $ 169.15 $1,130.00 $ 971.50 $ - 3 0 77 F CARE $ 4,992.01 $ 148.66 $ 569.50 $ 818.50 $ 272.25 4 0 73 F CARE $ 6,929.35 $ 679.25 $1,286.50 $ 1,135.50 $ 766.70 5 0 67 M CARE $ 5,595.42 $ 582.56 $ 714.00 $ 980.00 $ 848.75 3 0 86 M CARE $ 3,466.70 $ 78.15 $ 408.50 $ 187.00 $ 338.25 7 0 82 F CARE $ 7,289.77 $ 162.77 $ 821.50 $ 818.50 $ 825.85 7 0 84 F CARE $ 6,375.95 $ 275.30 $1,692.50 $ 93.50 $ 755.65 3 0 73 F BC $ 3,585.62 $ 276.29 $ 578.00 $ 951.50 $ 40.00 4 0 82 M CARE $ 5,970.45 $ 156.45 $ 711.50 $ 738.50 $1,084.85 8 0 62 F CARE $ 10,578.14 $ 696.94 $1,329.35 $ 783.65 $2,058.75 2 0 84 M CARE $ 2,223.60 $ 36.25 $ 229.00 $ 725.00 $ 253.10 3 0 89 F CARE $ 2,250.50 $ 182.70 $ 205.50 $ 117.50 $ 226.85 1 0 84 M CARE $ 1,644.55 $ 19.40 $ 142.00 $ 107.00 $ 137.00 4 0 81 F CARE $ 2,491.45 $ 84.45 $ 114.00 $ 93.50 $ 381.70 3 0 81 F CARE $ 1,691.50 $ 10.45 $ 114.00 $ 64.50 $ 12.95 6 0 78 M CARE $ 7,931.92 $ 746.06 $ 707.00 $ 200.50 $2,030.60 5 0 84 F CARE $ 5,121.97 $ 479.99 $ 981.35 $ 930.00 $ 314.90 5 0 37 M BC $ 6,940.75 $ 768.55 $1,791.50 $ 825.00 $ 922.10 7 0 62 M BC $ 12,088.08 $ 592.43 $ 971.80 $ 1,566.00 $2,170.60 1 0 80 F CARE $ 2,325.60 $ 101.50 $ 440.50 $ 107.00 $ 69.05 2 0 80 F CARE $ 4,452.78 $ 160.38 $ 276.50 $ 107.00 $ 720.00 4 0 73 M CARE $ 6,157.43 $ 193.61 $ 540.50 $ 725.00 $1,140.57 11 0 80 F CARE $ 21,474.90 $ 1,420.14 $2,302.00 $ 2,128.00 $2,765.60 3 2 80 F CARE $ 8,566.51 $ 446.11 $1,393.50 $ 214.00 $1,505.55 2 0 80 F CARE $ 4,910.27 $ 307.97 $ 707.00 $ 107.00 $ 820.70 1 0 81 F CARE $ 3,275.03 $ 152.28 $ 414.50 $ 107.00 $ 573.05 4 0 39 M CAID $ 12,080.81 $ 708.40 $ 971.50 $ 1,374.00 $ 881.10 6 0 86 M CARE $ 7,436.85 $ 242.70 $ 700.50 $ 1,183.00 $ 834.65 8 0 79 M CARE $ 15,624.20 $ 462.40 $2,372.00 $ 2,965.65 $2,097.17 4 0 87 M CARE $ 4,590.48 $ 414.40 $ 966.00 $ 187.00 $ 667.65 2 0 53 F CARE $ 3,232.63 $ 200.90 $ 320.00 $ 93.50 $ 425.80 3 0 83 F CARE $ 3,768.11 $ 216.01 $ 312.50 $ 196.50 $ 917.75 7 0 80 F CARE $ 9,862.26 $ 432.36 $1,504.00 $ 321.00 $1,555.25 7 0 79 F CARE $ 10,626.42 $ 449.47 $1,011.40 $ 107.00 $2,113.85 4 0 72 F CARE $ 6,967.99 $ 176.89 $1,062.00 $ 1,658.20 $ 221.60 3 0 77 F CARE $ 5,891.25 $ 260.65 $1,215.50 $ 107.00 $ 465.50 3 0 81 F CARE $ 4,756.91 $ 104.66 $ 893.50 $ 725.00 $ 87.10 9 0 67 F OTHR $ 8,096.93 $ 473.98 $ 862.50 $ 818.50 $1,708.65 4 0 80 M CARE $ 4,620.59 $ 178.59 $ 535.00 $ 296.00 $ 307.90 6 0 67 F OTHR $ 5,796.49 $ 472.74 $1,007.00 $ 93.50 $1,399.30 1 0 88 M CARE $ 1,483.39 $ 30.34 $ 172.00 $ 214.00 $ 136.30 1 0 88 F CARE $ 2,510.05 $ 82.45 $ 485.00 $ 188.50 $ 148.65 6 0 92 F CARE $ 10,185.83 $ 403.13 $1,054.50 $ 832.00 $1,920.75 3 0 85 F CARE $ 3,391.90 $ 49.60 $ 588.50 $ 725.00 $ 44.45 5 0 85 M CARE $ 8,418.13 $ 281.48 $ 758.00 $ 93.50 $ 75.20 3 0 80 M CARE $ 4,346.47 $ 108.11 $ 411.00 $ 725.00 $ 266.05 2 0 98 F CARE $ 2,043.85 $ 49.20 $ 214.00 $ 186.50 $ 268.55 3 0 74 F CARE $ 2,594.85 $ 131.60 $ 496.00 $ 155.50 $ - 5 0 77 M CARE $ 5,499.36 $ 153.91 $ 289.50 $ 660.00 $ 528.20 9 0 53 F CARE $ 11,244.45 $ 500.30 $ 657.00 $ 738.50 $1,154.80 7 0 93 M CARE $ 6,565.55 $ 710.00 $ 725.00 $ 117.50 $ 793.10 4 0 83 F CARE $ 6,031.15 $ 294.60 $1,313.00 $ 351.25 $ 684.15 7 0 80 M CARE $ 4,912.76 $ 468.01 $ 333.50 $ 187.00 $ 930.65 3 0 79 M CARE $ 6,182.45 $ 234.85 $ 843.50 $ 832.00 $ 304.30 3 0 87 F CARE $ 4,218.95 $ 183.45 $ 309.50 $ 99.00 $ - 16 0 59 M CARE $ 40,231.27 $ 2,768.32 $4,618.00 $ 1,609.00 $8,792.50 3 0 81 F CARE $ 3,608.95 $ 290.77 $ 457.50 $ 941.00 $ 225.90 4 0 94 F CARE $ 3,041.44 $ 109.59 $ 484.00 $ - $ 569.00 1 0 33 F CAID $ 1,581.93 $ 141.78 $ 539.50 $ 107.00 $ 230.75 2 0 78 F CARE $ 1,468.48 $ 175.18 $ - $ - $ 237.65 2 0 29 F CARE $ 2,294.55 $ - $ 209.00 $ 187.00 $ 688.75 2 0 80 F CARE $ 7,138.72 $ 402.98 $1,317.50 $ 300.50 $ 261.45 3 0 63 F INS $ 3,845.96 $ 182.31 $ 443.00 $ 93.50 $ 245.15 4 0 86 M CARE $ 5,355.23 $ 376.34 $ 890.90 $ 951.00 $ 361.65 4 0 96 M CARE $ 4,573.05 $ 563.40 $1,310.00 $ 296.00 $ 25.75 5 0 89 M CARE $ 5,023.11 $ 272.51 $1,039.50 $ 187.00 $ 683.45 5 0 80 M CARE $ 4,238.30 $ 112.15 $ 654.75 $ 725.00 $ 290.45 5 0 55 F CAID $ 6,885.73 $ 351.58 $ 838.50 $ 738.50 $ 792.80 5 0 73 M CARE $ 5,447.63 $ 224.98 $ 660.00 $ 912.00 $1,113.00 7 0 67 F CARE $ 6,257.66 $ 349.81 $ 761.85 $ 351.50 $ 708.90 2 0 75 M CARE $ 4,601.00 $ 655.64 $1,008.00 $ 214.00 $ 486.45Explanation / Answer
Answer to the question is as follows:
We have been given the fact that age is normally distributed.
We calculate from this data the params of normal distribution.
Mean is average of age = 74.9058
Stdev is 12.0782
P(X>=55) = 1-P(X<55) = 1-P(Z< (55-74.9058) / 12.0872) = 1-.0498 = .9502
P(X<45) = P(Z< (45-74.9058) / 12.0872) = .0067
P(45<X<55) = P(X<=55) - P(X<45) = .9502-.0067 = .9435
P(45<X<55) = ?