Standard Normal Curve Areas (page 1) Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z = 0 and a positive value of z. Z A Z A Z 0.118 0.60 0.00 0.000 0.30 0.01 0.004 0.31 0.02 0.008 0.03 0.012 0.33 0.04 0.016 0.34 0.05 0.020 0.35 0.06 0.024 0.36 0.07 0.028 0.37 0.144 0.67 0.08 0.032 0.38 0.148 0.68 0.09 0.036 0.39 0.152 0.69 0.10 0.040 0.40 0.155 0.70 0.11 0.044 0.41 0.12 0.122 0.61 0.32 0.126 0.62 0.129 0.63 0.133 0.64 0.137 0.65 0.141 0.66 0.159 0.71 0.42 0.163 0.72 0.048 0.166 0.73 0.13 0.052 0.43 0.14 0.056 0.44 0.170 0.74 0.15 0.060 0.45 0.174 0.75 0.16 0.064 0.46 0.177 0.76 0.17 0.067 0.47 0.181 0.77 0.18 0.071 0.48 0.184 0.78 0.19 0.075 0.49 0.188 0.79 0.20 0.079 0.50 0.191 10.80 0.21 0.083 0.51 0.22 0.087 0.52 0.23 0.091 0.53 0.24 0.095 0.54 0.25 0.099 0.55 0.26 0.103 0.56 0.27 0.106 0.57 0.28 0.110 0.58 0.219 0.88 0.29 0.114 0.59 0.222 0.89 0.195 0.81 0.198 0.82 0.202 0.83 0.205 0.84 0.209 0.85 0.212 0.86 0.216 0.87 Standard Normal Curve Areas (page 2) Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z=0 and a positive value of z. N 1.80 A z A Z 0.464 2.10 0.482 2.40 0 z Z A A z A Z 0.226 0.385 1.50 0.316 0.319 0.321 1.22 1.20 1.21 0.387 1.51 0.389 1.52 0.90 0.229 0.91 0.232 0.92 0.236 0.93 0.324 1.23 0.391 1.53 0.239 0.94 0.326 1.24 0.393 1.54 0.242 0.95 0.329 1.25 0.394 1.55 0.331 1.26 0.396 1.56 1.27 0.398 1.57 0.336 1.28 0.400 1.58 0.245 0.96 0.249 0.97 0.334 0.252 0.98 0.255 0.99 0.258 1.00 0.341 1.30 0.261 1.01 0.344 1.31 0.346 1.32 0.339 1.29 0.401 1.59 0.403 1.60 0.405 1.61 0.264 1.02 0.407 1.62 0.267 1.03 0.348 1.33 0.408 1.63 0.351 1.34 0.410 1.64 0.353 1.35 0.411 1.65 0.270 1.04 0.273 1.05 0.276 1.06 0.279 1.07 0.413 1.66 0.415 1.67 0.282 1.08 0.416 1.68 0.355 1.36 0.358 1.37 0.360 1.38 0.285 1.09 0.362 1.39 0.288 1.10 0.364 1.40 0.291 1.11 0.367 1.41 0.294 1.12 0.418 1.69 0.419 1.70 0.421 1.71 0.369 1.42 0.422 1.72 0.297 1.13 0.371 1.43 0.424 1.73 0.458 0.300 1.14 0.373 1.44 0.425 1.74 0.459 0.302 1.15 0.375 1.45 0.426 1.75 0.460 0.305 1.16 0.377 1.46 0.428 1.76 0.461 0.379 1.47 0.429 1.77 0.462 0.308 1.17 0.311 1.18 0.313 1.19 0.381 1.48 0.431 1.78 0.462 0.383 1.49 0.432 1.79 0.463 J 0 A 0.492 2 A 2.70 0.497 N~ Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. A 0.433 0.434 0.436 0.437 Z 3.00 0.438 0.439 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 0.457 Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. A Z A 0.499 3.30 0.500
Standard Normal Curve Areas (page 1) Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z = 0 and a positive value of z. Z A Z A Z 0.118 0.60 0.00 0.000 0.30 0.01 0.004 0.31 0.02 0.008 0.03 0.012 0.33 0.04 0.016 0.34 0.05 0.020 0.35 0.06 0.024 0.36 0.07 0.028 0.37 0.144 0.67 0.08 0.032 0.38 0.148 0.68 0.09 0.036 0.39 0.152 0.69 0.10 0.040 0.40 0.155 0.70 0.11 0.044 0.41 0.12 0.122 0.61 0.32 0.126 0.62 0.129 0.63 0.133 0.64 0.137 0.65 0.141 0.66 0.159 0.71 0.42 0.163 0.72 0.048 0.166 0.73 0.13 0.052 0.43 0.14 0.056 0.44 0.170 0.74 0.15 0.060 0.45 0.174 0.75 0.16 0.064 0.46 0.177 0.76 0.17 0.067 0.47 0.181 0.77 0.18 0.071 0.48 0.184 0.78 0.19 0.075 0.49 0.188 0.79 0.20 0.079 0.50 0.191 10.80 0.21 0.083 0.51 0.22 0.087 0.52 0.23 0.091 0.53 0.24 0.095 0.54 0.25 0.099 0.55 0.26 0.103 0.56 0.27 0.106 0.57 0.28 0.110 0.58 0.219 0.88 0.29 0.114 0.59 0.222 0.89 0.195 0.81 0.198 0.82 0.202 0.83 0.205 0.84 0.209 0.85 0.212 0.86 0.216 0.87 Standard Normal Curve Areas (page 2) Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z=0 and a positive value of z. N 1.80 A z A Z 0.464 2.10 0.482 2.40 0 z Z A A z A Z 0.226 0.385 1.50 0.316 0.319 0.321 1.22 1.20 1.21 0.387 1.51 0.389 1.52 0.90 0.229 0.91 0.232 0.92 0.236 0.93 0.324 1.23 0.391 1.53 0.239 0.94 0.326 1.24 0.393 1.54 0.242 0.95 0.329 1.25 0.394 1.55 0.331 1.26 0.396 1.56 1.27 0.398 1.57 0.336 1.28 0.400 1.58 0.245 0.96 0.249 0.97 0.334 0.252 0.98 0.255 0.99 0.258 1.00 0.341 1.30 0.261 1.01 0.344 1.31 0.346 1.32 0.339 1.29 0.401 1.59 0.403 1.60 0.405 1.61 0.264 1.02 0.407 1.62 0.267 1.03 0.348 1.33 0.408 1.63 0.351 1.34 0.410 1.64 0.353 1.35 0.411 1.65 0.270 1.04 0.273 1.05 0.276 1.06 0.279 1.07 0.413 1.66 0.415 1.67 0.282 1.08 0.416 1.68 0.355 1.36 0.358 1.37 0.360 1.38 0.285 1.09 0.362 1.39 0.288 1.10 0.364 1.40 0.291 1.11 0.367 1.41 0.294 1.12 0.418 1.69 0.419 1.70 0.421 1.71 0.369 1.42 0.422 1.72 0.297 1.13 0.371 1.43 0.424 1.73 0.458 0.300 1.14 0.373 1.44 0.425 1.74 0.459 0.302 1.15 0.375 1.45 0.426 1.75 0.460 0.305 1.16 0.377 1.46 0.428 1.76 0.461 0.379 1.47 0.429 1.77 0.462 0.308 1.17 0.311 1.18 0.313 1.19 0.381 1.48 0.431 1.78 0.462 0.383 1.49 0.432 1.79 0.463 J 0 A 0.492 2 A 2.70 0.497 N~ Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. A 0.433 0.434 0.436 0.437 Z 3.00 0.438 0.439 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 0.457 Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. A Z A 0.499 3.30 0.500
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:Standard Normal Curve Areas (page 1)
Areas under the Normal Curve
The column under A gives the
proportion of the area under the
entire curve that is between z = 0
and a positive value of z.
Z
A
z
A
z
0.60
0.00 0.000 0.30 0.118
0.01 0.004 0.31 0.122 0.61
0.02 0.008 0.32 0.126 0.62
0.03 0.012 0.33 0.129 0.63
0.04 0.016 0.34 0.133 0.64
0.05 0.020 0.35 0.137 0.65
0.06 0.024 0.36 0.141 0.66
0.028 0.37
0.032 0.38
0.07
0.144 0.67
0.148 0.68
0.08
0.09
0.036 0.39
0.152 0.69
0.10
0.040 0.40
0.155 0.70
0.11 0.044 0.41 0.159 0.71
0.12 0.048
0.42 0.163 0.72
0.166 0.73
0.170
0.74
0.174
Areas under the Normal Curve
The column under A gives the
proportion of the area under the
entire curve that is between z=0
and a positive value of z.
Z
1.80
1.81
1.82
1.83
0.13 0.052 0.43
0.14 0.056 0.44
0.15 0.060 0.45
0.75
0.16 0.064 0.46 0.177 0.76
0.17 0.067 0.47 0.181 0.77
0.18 0.071 0.48 0.184 0.78
0.19 0.075 0.49 0.188 0.79
0.20 0.079 0.50 0.191 0.80
0.21 0.083 0.51 0.195 0.81
0.22 0.087 0.52 0.198 0.82
0.23 0.091 0.53 0.202 0.83
0.24 0.095 0.54 0.205 0.84
0.25 0.099 0.55 0.209 0.85
0.26 0.103 0.56 0.212 0.86
0.27
0.216 0.87
0.28 0.110 0.58 0.219 0.88
0.106 0.57
0.29 0.114 0.59 0.222 0.89
Standard Normal Curve Areas (page 2)
A
z
0.464 2.10
0.465 2.11
0.466 2.12
0.466 2.13
1.84 0.467 2.14
1.85 0.468 2.15
1.86 0.469 2.16
1.87 0.469 2.17
1.88 0.470 2.18
1.89 0.471 2.19
1.90 0.471 2.20
1.91 0.472 2.21
1.92 0.473 2.22
1.93 0.473 2.23
1.94
1.95
1.96 0.475 2.26
1.97 0.476 2.27
0.474 2.24
0.474 2.25
1.98
0.476 2.28
0.477 2.29
0.477 2.30
1.99
2.00
0.478 2.31
0.478
2.01
2.02
2.32
2.03
0.479 2.33
2.04 0.479 2.34
A
0.482
0.483
z
2.40
2.41
0
0.483 2.42
0.483 2.43
0.484 2.44
0.484 2.45
0.485 2.46
0.485 2.47
0.485 2.48
0.486 2.49
0.486 2.50
Z
A
z
0.226
0.90
0.229 0.91
0.232 0.92
0.236 0.93
0.239 0.94
0.242 0.95
0.245 0.96
0.249 0.97
0.252
0.98
0.255 0.99
0.258 1.00
0.261 1.01
0.264 1.02
0.267 1.03
0.270 1.04
0.273 1.05
0.276
0.279
0.282
0.285
0
A
z
0.492 2.70
0.492 2.71
0.492 2.72
0.492 2.73
0.493 2.74
0.493 2.75
0.493 2.76
0.493 2.77
0.493 2.78
0.494 2.79
0.494 2.80
0.494 2.81
0.487 2.52 0.494 2.82
0.487 2.53 0.494 2.83
0.487 2.54
0.486 2.51
0.494
2.84
0.488 2.55
0.495
2.85
0.488 2.56
0.495
2.86
0.488 2.57
0.495 2.87
0.489 2.58
0.495 2.88
1.08
1.09
0.288 1.10
J
0.403 1.60
0.405 1.61
0.407
1.62
0.408
1.63
0.351 1.34 0.410 1.64
0.353 1.35 0.411 1.65
1.06 0.355 1.36 0.413 1.66
1.07 0.358 1.37
0.415 1.67
0.360 1.38
0.416 1.68
0.362 1.39
0.418 1.69
0.364 1.40
0.419 1.70
0.367 1.41
0.421 1.71
0.369
1.72
1.42 0.422
0.371 1.43 0.424 1.73
0.373 1.44
1.74
0.425
0.375 1.45 0.426 1.75
0.428 1.76
0.429 1.77
0.431 1.78
0.432 1.79
0.489 2.59
0.495 2.89
0.489 2.60 0.495 2.90
0.490 2.61
0.490 2.62
0.490 2.63
0.490
2.64
2.05 0.480 2.35 0.491 2.65
2.06 0.480 2.36
0.491 2.66
0.481 2.37
0.491 2.67
2.07
2.08
2.09 0.482 2.39 0.492 2.69
0.481 2.38
0.491 2.68
0.291 1.11
0.294 1.12
0.297 1.13
0.300 1.14
0.302 1.15
0.305 1.16 0.377 1.46
0.308 1.17 0.379 1.47
0.311 1.18 0.381 1.48
0.383 1.49
0.313 1.19
2
0.495 2.91
0.496
2.92
0.496 2.93
Because the curve is symmetric
about 0, the area between z = 0
and a negative value of z can be
found by using the corresponding
positive value of z
z.
0.496 2.94
0.496 2.95
0.496 2.96
A
z
0.316
1.20
0.319 1.21
0.321 1.22 0.389
0.496 2.97
0.496 2.98
0.496 2.99
A
Z
0.385 1.50
0.387 1.51
1.52
0.324 1.23
0.391 1.53
0.326 1.24
0.393 1.54
0.329 1.25 0.394 1.55
0.331 1.26 0.396 1.56
0.398 1.57
0.334 1.27
0.336 1.28 0.400 1.58
0.339 1.29
0.401 1.59
0.341 1.30
0.344 1.31
0.346 1.32
0.348 1.33
Z
A
Z
A
0.497 3.00
0.497 3.01
0.499 3.30
0.499 3.31
0.497 3.02
0.499 3.32
0.497 3.03
0.499 3.33
0.497 3.04
0.499 3.34
0.497 3.05 0.499 3.35
0.497 3.06
0.497 3.07
0.497 3.08
0.497 3.09 0.499 3.39
0.497 3.10
0.499 3.40
0.498 3.11
0.498 3.12
0.498 3.13
0.499 3.41
0.499 3.42
0.499 3.43
0.498 3.14
0.499 3.44
0.498 3.15
0.499 3.45
0.498 3.16
0.499 3.46
0.498 3.17
0.499 3.47
0.498 3.18
0.499 3.48
0.499 3.49
0.498 3.19
0.498 3.20
0.499 3.50
0.498 3.21
0.499 3.51
0.498 3.22
0.499 3.52
0.498 3.23
0.499 3.53
0.498 3.24
0.499 3.54
0.498 3.25
0.499 3.55
0.498 3.26
0.499 3.56
0.499 3.57
0.499 3.27
0.499 3.28
0.499
3.29
0.499 3.58
0.499 3.59
0.499 3.36
0.499 3.37
0.499 3.38
A
0.433
0.434
0.436
0.437
0.438
0.439
0.441
0.442
0.443
0.444
0.445
0.446
0.447
Because the curve is symmetric
about 0, the area between z = 0 and
a negative value of z can be found
by using the corresponding positive
value of z.
0.448
0.449
0.451
0.452
0.453
0.454
0.454
0.455
0.456
0.457
0.458
0.459
0.460
0.461
0.462
0.462
0.463
A
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
Transcribed Image Text:A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 12 ounces and standard deviation 0.6 ounce. Among a sample of
1000 of those peaches, about how many could be expected to have weights of at least 12 ounces?
Click here to see page 1 of the table for areas under the standard normal curve.
Click here to see page 2 of the table for areas under the standard normal curve.
The number of peaches expected to have weights of at least 12 ounces is
(Round to the nearest whole number as needed.)
C
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